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THE

PHYSICAL PAPERS

HENRY AUGUSTUS ROWLAND

THE

PHYSICAL PAPERS

HENRY AUGUSTUS ROWLAND

Ph. D.; LL. D. 1

Professor of Phyacs and Director of the Physical Laboratory in
The Johns Hopkins University

COLLECTED FOR PUBLICATION BY A
COMMITTEE OF THE FACULTY OF THE UNIVERSITY

BALTIMORE
The Johns Hopkins Press
1902

IIA Lib..

PRINTED BY

Company

HENRY AUGUSTUS ROWLAND

Born, Honesdale, Pennsylvania, November 27, 1848
Died, Baltimore, Maryland, April 16, 1901

.Doctor of riiiloso[)liy ('.Pli. 1).);, Jolms Hopkins University, 1880. (Hon-
oris Clausa.)

Doctor of Laws (LL. D.), Yale University, 1895.

Do(*tor oJ! Laws (LIj. D.), Princeton University, 189G.

Fellow or Member of

Tlio Jlritish Association for the Advancement of Science.

The IMiysical Society of London.

Tho IdiiloKophictil Soci(‘ty of Cambridge, England.

''riie Koyal Society of London.

Tlie Koyal Society of (Jiittingen.

Tlie (ii<)(Miian Academy of Natural Sciences, Catania, Sicily.

The Eroneh Diysical So<*.i(dy.

'J'lie French Aea<Ieniy of Sciences.

Tlie hit<‘rary and Philosophical Society of Manchester.

Tlie Jioyal LyiK^mn A<‘adeiny, Komc.

The Aca<leiny of S<uen<a*s, Stockholm.

Thi\ Italian Society of Siicetroscopists.

The Koyal So<uety of Ediiibiirgb.

Tin‘ Society of Arts, London.

'Pile lioyarAHtrononiical Society of England.

The Koyal Society of Lomhavdy.

Tin*. Koyal Tdiysiograplne Society of Lund.

I’lie Koyal Aiauhuuy of Seimiees, Kerliu.

'!l’he Koyal Aeadtuny of Selene<^s and Letters, Copenhagen.

TIki Aineriean Philosoiihieal {Society, J^hihulelidiia.

'Phe American Aeaileiny of Arts and Seienecs, Boston.

The National Aeadtuny of Seituiees, VVashhigton.

'Phe Amtu'iean PliysieSil Soeiid.y,- -its first lYcsidciit.

The Astronoiuieal’and A.sI.rophysieal Society of America.

'Dolcfriiic of ilu* Hnil.cil Siulcs (lovcniiiiont lo tlu-

I nl<*rnalionaI Congr<*ss of Fleet rieians, l^aris, 38.S1.

1 ntcuMiational (’ongri'ss for the Diderniination of Tillectrical Units, Paris,
IS.SJL Appointed OlfKMU' of the Legion of Honor of Frajice.
Kh»etri<*al Congn'ss, Idiiladelphia, 1 SSI, -—President.

International (Miamlxu- of Ikdeptes for the Determination of Electrical
Cnits, (Miieago, Kresident.

Pkizks and Mmdals.

Kinnford Medal, American Aeailemy of Arts and Sciences.

Drapm* Meilal, National Aeailemy of vS(5icnces.

MattiMieei Mc'dnI.

Prize a\vard(‘d l)y 11»<’! Vmiidian Institute in coniiietition for a critical
fiapiM* on th<* Meehaineal E(|iiivalent. of Heat.

PREFACE

Shortly after the death of Professor Howland in April, 1901, a com-
initteo of the Faculty of The Johns llophins University was appointed
by President G-ilinim to suggest to the Trustees of the University a plan
for a memorial of their colleague. The committee, consisting of Pro-
fessors Roniscn, Welch and Ames decided to rocouiinond that a volnmo
bo prepared containing the ]>hysical papers and addresses of Professor
Rowland, and also a detailed description of the dividing engines which
had been designed and eonstnictcd l)y him for the pnrposo of ruling
ditTractioii gratings, and that this volume bo published by the Univorsity
Press. This recommendation was approved by tlu^ Trustees of the
Univorsity; and the same comniittoe, with the addition, of Professor
R. W. Wood, was empowered to prepare the volume for ])ublieatlon-
The editorial sui)orvlsion has been mainly undertaken by Professor
Joseph S. Ames.

In deciding upon Iho scope of the pToi)()sod volnnic, it was thought
best to include only the distinctly i)hyBieal papers, inasniiicli as Pro-
fessor Rowland himself on several occasions when the (luesiion of the
colh'ctiou of liis sci(‘iitific j)ai)ers \Yas raised, had e.vpresscul himself as
()p]>()sed to the repuhlication of the pnredy nmUicmmtiea.1 ernes. It was
also decided to omit tables of wave-lengths, as tlu^so are extremely
bulky, and copies can be easily oldaiiied. JVofessor Rowland kvtt many
thousand i)agcs of manuscript notes and outlines of lectures, but none
of this material was rt^ady for jniblicaiion, and the ciomrnittoe were not
in a position to iindcrtakcj the task of its pro])arati()n. No attempt has
l)i‘cn made to include a biography of Professor Howland, for this wo\ikl
])roporly form a volume l)y itself, and would nupiiro much time for its
preparation. TIkm'o was at hand, moreover, the momorial address of
Dr. Mendenhall, which tells so well, tlu)ngh briefly, the story of his life.

vi Peefaoe

It was with difficulty, and only after a careful examination of many
hundred yolumes of sdentifie journals and transactions, that the com-
mittee were able to obtain copies of all of Professor Eowland^s numerous
and scattered articles; but they are convinced that no paper of import-
ance has escaped their notice. In preparing for publication these me-
moirs and addresses, no alterations other than typographical have been
made.

For permission to reprint some of the most valuable papers, thanks
are due to various publishers. The committee wish especially to express
their appreciation of the kindness of Messrs. A. and C. Black, and of
The Times (London) for permission to reprint from the Encyclopaedia
Britannica the articles on ^^The Screw and on ^^Diffraction Gratings,
and of the Engineering Magazine Company, of KTew York, for permis-
sion to reprint the article on Modem Theories as to Electricity.”

The committee acknowledge their indebtedness also to Mr. N. Mur-
ray, Librarian of The Johns Hopkins University, who has personally
superintended the details of publication, and whose advice has been
often needed. The proofs have been revised by Mr. E. P. Hyde, Fellow
in The Johns Hopkins University, who has thus been of the greatest
assistance to the committee.

The Johns Hopkins University,
Baltimore, Maryland,
Dboembek 1 , 1903 .

CONTENTS

Pi.ajs

PREFACE V

ADDRESS BY DR. T. C. IMENDENIIALL 1

SCIENTIFIC PAPERS 11)

Pakt 1. Eauly Papers. 21

*1. The Vortex l*roblem 2:j

Seleiitmc Ainorlcftii XII 1, KUS, 1S(»5.

2. l^aine’s Eleetro-mag'netic Eng’iJie 24

Sclentlllc Ainorlcaii XXV, 21, 1871.

3. Illusti’atioii of lleROiianoes and Actions of ii Similar Nature 28

Journal of the Franklin Institute XOIV, 27.V27.S, 1872.

4. On the Auroi*al Spectimm 31

Ainerlean Journal of Solonce (:’»), V, 320, 1873.

Part II. I^Iaonetism ani> ErjiCTiuorrY, 83

0. On Ma^jnetic Permeability, and the Maxi mum of Magnetism of lx*on,

Steel and Nickel 35

Philosophical Magazine (4), XLVl, 140-150, 1873.

0. On the Magnetic Perincaljility and Ma.Kiinum of Magnetism of Nickel

and Cobalt 5()

Philosophical Magazine (4), XI.VIII, 321-340, 1874.

7. On a new Dianiagnelic Atiaelimeiit to the Jiuntern, wil.U a Note on

the TJieory of the Oscillations of liKliictively Magnetized Bodies.. 75
AnKM’lean Journal of S<*lence (3), IX, 357-301, .KS75.

8. Notes on Magnetic .Distribution 80

lMvKU*o<lliig.s of llu‘ American Aiuulciiiy of Arts uiul Sciences, XI, 101, 102,

1870.

9. Not<‘. on Kolilraiiseirs Delennination of the Absolute Value of tlio

Siemens Me.nuiry Unit of Eleetrieal Resistniiee 82

PhlloHophlcal Mugazlm* (4), b, 101-PKI, :1875.

10. Preliminary Note on a Magnetic. Proof Plane 85

Aiiierlcau Journal of Si'lence C3), X, 14-17, 1875.

* Tho numborfl rof(<r to corrospoadiiig ones in the bibliography, page 6«l.

viii

Contents

PAGB

11. Studies on Magnetic Distribution 89

American Journal of Science (3), X, 326-335, 451-451), 1S75.

Ibid., XI, 17-29, 103-108, 1876.

Philosophical Magazine (4), L, 267-277, 848-867, 1876.

12. On the Magnetic Effect of Electric Convection 128

American Journal of Science (3), XV, 30-38, 1878.

13. Note on the Magnetic Effect of Electric Convection 138

Philosophical Magazine (6), VEt, 442-443, 1879.

14. Note on the Theory of Electric Absorption 139

American Journal of Mathematics, I, 53-68, 1878.

15. Hesearch on the Absolute Unit of Electrical Hesistance 145

American Journal of Science (3), XV, 281-201, 325-336, 430-439, 1878.

17. On Professors Ayrton and Perry’s New Theory of the Earth’s Mag-

netism, with a Note on a New Theory of the Aurora 179

Philosophical Magazine (6), VIII, 102-106, 1870.

Proceedings of the Physical Society, III, 93-98, 1879.

18. On the Diamagnetic Constants of Bismuth and Calc-spar in Absolute

Measure. By H. A. Rowland and W. W. Jacques 184

American Journal of Science (3), XVIII, 360-371, 1870.

19. Preliminary Notes on Mr. Hall’s recent Disco^'ery 197

American Journal of Mathematics, II, 354-3.50, 1870.

Philosophical Magazine (6), IX, 432-434, 1880.

Proceedings of the Physical Society, IV, 10-13, 1880.

23. On the Efficiency of Edison’s Electric Light. By H. A. Rowland and

G. E. Barker 200

American Journal of Science (3), XIX, 337-339, 1880.

27. Electric Absorption of Crystals. By H. A. Rowland and E. L.

Nichols 204

Philosophical Magazine (5), XI, 414-419, 1881.

Proceedings of the Physical Society, IV, 215-221, 1881.

28. On Atmospheric Electricity 312

Johns Hopkins University Circulars No. 10, pp. 4, 5, 1882.

34. The Determination of the Ohm. Extract from a letter to the Inter-

national Congress at Pai'is, 1884 217

ProcGs-Verhaux, DeuxlOme Session, p. 37. I'aris, 1884.

35. The Theory of the Dynamo 310

Report of the Elcctidcal Conference ait l*lilln<lclphla In November, 1884,
pp. 72-83, 00, 91, 104, 107. ■Washington, 1886.

36. On Lightning Protection 230

Report of the Electrical Conference at Philadelphia in November, 1884,
pp. 172-174.

37. On the Value of the Ohm 239

La Lumlfire Electrlque, XXVI, pp. 188, 477, 1887.

C0NTKNT8

FAQB

38. On a Simple and Convenient Form of Water-battery 241

American Journal of Science (3), XXXIII, 147, 1887.

Philosophical IMagazliio (5), XXIII, 303, 1887.

Johns Ilopkins UnlverHity Cinnilars No. 57, p. SO, 1887.

40. On an Explanation of the Action of a Mapfiiet on C^-heinical Action.

By H. A. Rowland and Louis Bell 242

American Journal of Science (3), XXXVI, ,30-47, 1888.

PhlloHophical Mairazlne (5), XXVI, 105-114, 1888.

43. On the Electromagnetic Effect of Convection-Currents. By H. A.

Rowland and C. T. Ilutchinsoii 251

Philosophical Maffazlne (5), XXVH, 445-400, 1,880.

44. On the Ratio of the Electro-static toi the Electro-magnetic Unit of

Electricity. By 11. A. Rowland, K. II. Hall, and L. B. Flcte.hcr. .. 206
American Journal of S<lonce (.3). XXXVIII, 280-208, 1880.
l»hlloHophl(;al MawKlne (5), XXVIIt, .304-315, 1880.

47. Notes on the Tlieory of the Transformer 276

l^hlloHophical xMapizIne (5), XXXIV, 54-57, 1802.

ElecU'lcal Worlil, XX, 20, 1802.

Johns Ilopkins t.Tnlvorsity OirciUars No. OS), pp. 101, 105, 1802.

48. Notes on the Effect of llaiunonics in the Tninsmissiou of Power by

Alternating Currents 280

Electrical World, XX, 308, 1802.

lia Ijuiniere Klectrl<iue, XLVll, •J2-4-1, 1803.

53. Modern ThoorU‘s m to Electricity 285

The Enj?iiu*orinjjf Maf^azlue, V'!!!, 5S0-5SMJ, 1805.

60. Electrical ^Moasurenient by Alternating OiirrcntH 294

Aim*rl<‘au .Tounval of 8cl(*n<‘e (4), IV, 42S)-1I8, IHOT.

IMiIlosoidilcal Majynzlne (5). NLV', SMI-85, 1808.

62. Electrical ’McasniHuncnts. By H. A. Rowland and T. 1). iVnuiman.. 314

American Journal <if Science (4), VIII, .3,5-,57, .1800.

63. Resistance to Ethereal jMoiion. By 11. A. Rowland, N. E. (liUie.rt and

P. C. hlcJ unchin 338

Johns Ilopkins ITnIvcrslly (Mnndars No. 1.46, p. 60, 1000.

Part III. I! mat. ,341

16. On the Mechanical Eqnivahnit of Heat, with Subsidiary RcK(3irchcs
on tlu^ Variation of the Mercurial from th<^ Air-Thcriuonnd.cr and

on the Variatitvn of ihc Specific Il<‘at of Water 343

l‘rocc<MllnKS of the Aimu’lcan Academy of Arts an<l Sidcnccs, XV, 75-200,

1880.

21. ApiWindix to PajXM- on the Mechanical Eipiivalent of Beat, (Jontain-

ing the (Comparison wit.h Dr. Joule’s Thermometer 460

l*roet*edini;s of the American Academy of Arts nn<l Sidenccs, XVI, ,38-45,
1881.

20. Physical Laliorutory; CComparison of Standards i 477

Johns Ilopkins Bniverslly (Urcuhirs No. .3, p. 31, 1880.

Contents

26. On Geissler Thermometers

American Journal of Science (3), XXI, 461-463, 1881.

PAOB

481

Paet IV. Light. 486

29. Preliminary Notice of the Hesnlts Accomplished in the Manufacture

and Theory of Gratings for Optical Purposes 487

Johns Hopkins TTnlverslty Olrculars No. 17, pp. 248, 249, 1882.

Philosophical Magazine (4), XIII, 469-474, 1882.

Nature, 26. 211-213, 1882.

30. On Concave Gratings for Optical Purposes 492

American Journal of Science (3), XXVI, 87-98, 1883.

Philosophical Magazine (5), XVI, 197-210, 1883.

31. On Mr. Glazebrook’s Paper on the Aberration of Concave Gratings. 605

American Journal of Science (3), XXVI, 214, 1883.

Philosophical Magazine (5), XVI, 210, 1883.

33. Screw 506

Encyclopaedia Brltannica, Ninth Edition, Vol. 21.

39. On the Relative Wave-lengths of the Lines of the Solar Spectrum . . . 512
American Journal of Science (3), XXXIII, 182-190, 1887.

Philosophical Magazine (5), XXHI, 257-266, 1887.

41. Table of Standard VVave-lengths 517

Philosophical Magazine (5), XXVH, 479-484, 1880.

42. A Pew Notes on the Use of Gratings 510

Johns Hopkins University Circulars No. 73, pp. 73, 74, 1880.

46. Report of Progress in Spectrum Work

The Chemical News, LXIII, 133, 1891.

Johns Hopkins University Circulars No. 86, pp. 41, 42, 1801
American Journal of Science (3), XLI, 243, 244, 1891.

49. Gratings in Theory and Practice

Philosophical Magazine (6), XXXV, 307-410, 1803.
Astronomy and Astro-Physics, XH, 120-149, 1803.

50. A New Table of Standard Wave-lengths r> ir)

Philosophical Magazine (6), XXXVI, 40-76, 1803.

Astronomy and Astro-Physics, XII, 321-347, 1803.

51. On a Table of Standard Wave-lengths of the Spectral Lines r> is

Memoirs of the American Academy of Arts and Sciences, XII, 101-180,

1806.

52. The Separation of the Rare Earths r)65

Johns Hopkins University Circulars No. 112, pp. 73, 74, 1804.

57. Notes of Observation on the Rontgen Rays. By H. a! Rowland, N.

R. Carmichael and L. J. Briggs 571

American Journal of Science (4), I, 247, 248, 1896.

Philosophical Magazine (5), XLI, 381-382, 1806.

521

Contents

PAGH

58, Notes oil Kirntgen Rays. By H. A. Rowland, N. R. Canaioliael and

L. J. Briggs 573

Blectrlciil World, XXVII, 452, 1890.

59. The Rontgen Ray and its Relation to Physics 576

TrunsjietionH of the Anierlcun Institute of Hlectrlcal Engineers, XHI,
403-410, 430, 431, ISilO.

04. BilTraction Gratings 587

Encyclopaedia llrlt’annlea, New Volumes, III, 458, 459, 1902.

ADDRESSES 591

1. A Plea for Pure Science. Address a« Vice-President of Section B of

the Anicricaii Association for the Advancement of Science, Minne-

ai)olis, August 15, 1883 593

l»ro<'ctMlings of the Ainorlcan AHSociatlon for the Advancement of Science,
XXXXT, 105-120, 1883.

S<*icuco, ir, 242-250, lSa‘t.

Journal of the Franklin Institute, OXVI, 270-209, 1883.

2. The Physical Laboratory in Modern Education. Address for Com-

niomoratioii Day of th<^ Johns ITopkIns University, February 22,

1880 014

Johiifl Hopkins XFiilvorslty Circulars No. 50, i)p, 10JM05, 1880.

3. Address as Prosi<l<Mit of the Electrical Conference at Philadelphia,

S(‘pteinb(‘r S, 1884 619

Ueport; of lli<' El<M,t(,rIcal Conference at Philadelphia in September, 1884,
Washington, 1,88().

4. TJie lOIoetrical and Magnetic Discoveries of Faraday. Address at

'rht» Opening of the El<»etriea.l Club House of New York City, 1888. 638
Uloctrlcnl IK'Vlew, Fob. 4, 1888,

5. On Mo<U‘rn Vi<*ws wil.li Respect to Electric Currents. Address Be-

fore tin*, AnuMMcan Institute of Electrical Engineers, New York,

May 22, 1880 653

'rraiisjwllons of the Ainerloan Iiisl.Uute of Mlectrlcal Engineers, VI, 342-
3.57, 188i).

r>, Th<‘ niglu'st. .\ini of tluj PliyHicist. Address as l^rcsident of the

Anu*ri<‘aa Physical Soeiety, New York, October 28, 1899 668

8<4cncc. X, 825-KW, 18JM).

Ann*rl<^un Journal of Science (4), VIH, 40,1-Hl, 18t)9.

Johns Hopkins University CIreulurs No. 143, pp. 17-20, 1900.

lUlUdOCJRAPlIY

DESCRIPTION OK THE DIVIDING ENGINES DESIGNED BY PRO-
FESSOR ROWLAND

INDEX,

699

HENRY A. ROWLAND

COMMEMORATIVE ADDRESS

DR. THOMAS C. MENDENHALL

\peUm'ed before an aemnbly of friend^ Baltimore^ Oeioher 20, 1901.]

In reviewing the scientific work of Professor Rowland one is most
impressed by its originality. In quantity, as measured by priuted page
or catalogue of titles, it has been exceeded by many of his contem-
poraries; in quality it is equalled by that of only a very, very small
group. The entire collection of his important papers does not exceed
thirty or forty in number and his unimportant papers were few. When,
at the unprecedentedly early age of thirty-three years, he was elected
to membership in the National Academy of Sciences, the list of his
published contributions to science did not contain over a dozen titles,
but any one of not less than a half-dozen of these, including what may
properly bo called hie very first original investigation, was of such
quality as to fully entitle him to the distinction then conferred.

Fortunately for him, and for science as well, ho lived during a period
of almost unparalleled intellectual activity, and his work was done
during the last quarter of that century to which we shall long turn
with admiration and wonder. During those twenty-five years the num-
ber of industrious cultivators of his own favorite field increased enor-
mously, duo in large measure to the stimulating eftoct of his own enthu-
siasm, and while there was only here and there one possessed ot the
divine afflatus of true genius, there were many ready to labor most assid-
uously in fostering the growth, development, and final fruition of germs
which genius stopped only to plant. A proper estimate of the magni-
tude and extent of Rowland’s work would require, therefore, a careful
examination, analytical and historical, of the entire mass of contribu-
tions to physical science during the past twenty-five years, many of
his own being fundamental in character and far-reaching in their influ-
ence upon the trend of thought, in theory and in practice. But it was
1

Hbnet a. Eowland

quality, not quantity, that he himself most esteemed in any perform-
ance; it was quality that always commanded his admiration or excited
liiTn to keenest criticism; no one recogmzed more quickly than he a
real gem, however minute or fragmentary it might he^, and by quality
rather than by quantiiy we prefer to judge his work to-day, as he would
himself have chosen.

Eowland^s first contribution to the literature of science took the
form of a letter to The Scientific American, written in the early Autumn
of 1865, when he was not yet seventeen years old. Much to his sur-
prise this letter was printed, for he says of it, I wrote it as a kind of
joke and did not expect them to publish it." ISTeither its humor nor
its sense, in which it was not lacking, seems to have been appreciated
by the editor, for by the admission of certain typographical errors he
practically destroyed both. The embryo physicist got nothing but a
little quiet amusement out of this, but in a letter of that day he de-
clares his intention of some time writing a sensible article for the
journal that so unexpectedly printed what he meant to be otherwise.
This resolution he seems not to have forgotten, for nearly six years
later there appeared in its columns what was, as far as is known, his
second printed paper and his first serious public discussion of a scientific
question. It was a keen criticism of an invention which necessarily
involved the idea of perpetual motion, in direct conflict with the great
law of the Conservation of Energy which Eowland had already grasped.
It was, as might be expected, thoroughly well done, and received not a
little complimentary notice in other journals. This was in 1871, the
year following that in which he was graduated as a Civil Engineer from
the Eensselaer Polytechnic Institute, and the article was written while
in the field at work on a preliminary railroad survey. A year later,
having returned to the Institute as instructor in physics, he published
in the Journal of the FranTdin Institute an article entitled " Illustra-
tions of Eesoiiances and Actions of a Similar Nature," in which he
described and discussed various examples of resonance or sympa-
thetic" vibration. This paper, in a way, marks his admission to the
ranks of professional students of science and may be properly con-
sidered as his first formal contribution to scientific literature; his last
was an exhaustive article on spectroscopy, a subject of which he, above
all others, was master, prepared for a new edition of the Encyclopjedia
Britannica, not yet published. Early in 1873 the American Journal of
Science printed a brief note by Eowland on the spectrum of the Aurora,
sent in response to a kindly and always appreciated letter from Pro-

OoiOtEMCOBATXTE ASDBBSS

fessor George F. Barker, one of the editors of that jom-nal. It is inter-
esting as Tnar king the beginning of his optical work. For a year, or
perhaps for several years previous to this time, however, he had been
busily engaged on what proved to he, in its influence upon his future
career, the most important work of his life. To clhnb the ladder of
reputation and success by simple, easy steps might have contented
Eowland, but it would have been quite out of harmony with his bold
spirit, his extraordinary power of analysis and his quick recognition of
the relation of things. By the aid of apparatus entirely of his own
construction and by methods of his own devising, he had made an inves-
tigation both theoretical and experimental of the magnetic permea-
bility and the maximum magnetization of iron, steel and nickel, a
subject in which he had been interested in his boyhood. On June 9,
1873, in a letter to his sister, he says : “ I have just sent ofiE the results
of my experiments to the publisher and expect considerable from it;
not, however, filthy lucre, but good, substantial reputation.” What
he did get from it, at first, was only disappointment and discourage-
ment. It was more than once rejected because it was not understood,
and finally he ventured to send it to Clerk Maxwell, in England, by
whose keen insight and profound knowledge of the subject it was
instantly recognized and appraised at its full value. Eegretting that
the temporary suspension of meetings made it impossible for him to
present the paper at once to the Eoyal Society, Maxwell said ho would
do the next best thing, which was to send it to the PMlosoplneal Maga-
zim for immediate publication, and in that journal it appeared in
August, 1873, Maxwell himself having corrected the proofs to avoid
delay. The importance of the paper was promptly recognized by
European physicists, and abroad, if not at home, Eowland at once took
high rank as an investigator.

In this research he unquestionably anticipated all others in the dis-
covery and announcement of the beautifully simple law of the magnetic
circuit, the magnetic analogue of Ohm’s law, and thus laid the founda^
tion for the accurate measurement and study of magnetic permea-
bility, the importance of which, both in theory and practice during
recent years, it is difficult to overestimate. It has always seemed to
me that when consideration, is given to his age, his training, and the
conditions under which his work was done, this early paper gives a
better measure of Eowland’s genius than almost any performance of
his riper years. During the next year or two he continued to work
along the same lines in Troy, publishing not many, but occasional.

Hbitbt a. Eowland

additions to and developments of his first magnetic research. There
was also a paper in which he discussed Kohlrausch’s determination of
the absolute value of the Siemens unit of electrical resistance, fore-
shadowing the important part which he was to play in later years in the
final establishment of standards for electrical measurement.

In 1876, having been appointed to the professorship of physics in
the Johns Hopkins University, the facuHy of which was just then
being organized, he visited Europe, spending the better part of a year
in the various centres of scientific activity, including several months at
Berlin in the laboratory of the greatest Continental physicist of his
time, von Helmholtz. While there he made a very important investi-
gation of the magnetic effect of moving electrostatic charges, a question
of first rank m theoretical interest and significance. His manner of
pla nnin g and executing this research made a marked impression upon
the distinguished Director of the laboratory in which it was done, and,
indeed, upon all who had any relations with Eowland during its pro-
gress. He found what von Helmholtz himself had sought for in vain,
and when the investigation was finished in a time which seemed incred-
ibly short to his more deliberate and painstaking associates, the Director
not only paid it the compliment of an immediate presentation to the
Berlin Academy, but voluntarily met all expenses connected with its
execution.

The publication of this research added much to Eowland’s rapidly-
growing reputation, and because of that fact, as well as on account of
its intrinsic value, it is important to note that his conclusions have
been held in question, with varying degrees of confidence, from the day
of their announcement to the present. The experiment is one of great
difficulty and the effect to be looked for is very small and therefore
likely to be lost among unrecognized instrumental and observational
errors. It was characteristic of Eowland’s genius that with compara-
tively crude apparatus he got at the truth of the thing in the very start.
Others who have attempted to repeat his work have not been uniformly
successful, some of them obtaining a wholly negative result, even when
using apparatus apparently more complete and effective than that first
employed by Eowland. Such was the experience of Lecher in 1884,
but in 1888 Eoentgen confirmed Eowland’s experiments, detecting the
existence of the alleged effect. The result seeming to be in doubt,
Eowland himself, assisted by Hutchinson, in 1889 took it up again,
using essentially his original method but employing more elaborate and
sensitive apparatus. They not only confirmed the early experiments.

COMMEMOEATIVB ADDRESS

but were able to show that the results were in tolerably close agreement
with computed values. The repetition of the experiment by liimstedt
in the same year resulted in the same way, but in 1897 the genuineness
of the phenomenon was again called in question by a series of experi-
ments made at the suggestion of Lippmann, who had proposed a study
of the reciprocal of the Howland effect, according to which variations
of a magnetic field sliould produce a movement of an electrostatically
charged body. This investigation, carried out by Cr6Tnieu, gave an
absolutely negative result, and because the method was entirely differ-
ent from that employed by Howland and, therefore, unlikely to be
subject to the same systematic errors, it naturally had much wedght
with those who dotibted his original conclusions. Realizing the neces-
sity for additional evidence in corroboration of his views, in the Pall
of the year 1900, the problem was again attacked in his own laboratory
and lie had the satisfaction, only a short time before his death, of
seeing a complete confirmation of the results ho had announced a
quarter of a century earlier, concerning which, however, th(‘ro had
never been the slightest doubt in his own mind. It is a further satis-
faction to his friends to know that a very recent investigation at the
.rofferson Physical Laboratory of Harvard University, in which Row-
land’s methods were modified so as to meet effectively the objections
made by his critics, has resulted in a complete verification of his
conclusions.

On his return from Europe, in 1876, his time was much occupied
with the beginning of the active duties of his professorship, and
especially in putting in order the equipment of the laboratory over
winch ho was to preside, much of which he had ordered while in Europe.
Tn its arrangement great, many of his friends thought unduci, i>romi-
nence was given to the workshop, its macliinery, tools, and espcHually
the men who wore to ])o employed in it. Tie planned wisely, however,
for he meant to see to it that much, perhaps most, of the work under
his direction shonld he in the nature of original investigatioTi, for the
successful oxcention of whi<!h a well-manned and equipped workshop is
worth more than a storehouse of appanitais alfoady d(*sign(?d aud used
by others.

He shortly found leisure, however, to plan an olaborai.e r(‘stjarch u])on
the Mechanical Equivalent of Heat, and to design and supervise* the
construction of the necessary apparatus for a determinatioTi of the
numerical value of this most important physical constant, which he
determined should bo exhaustive in character and, for some time to

Hbnkt a. Eowlamd

come, at laast, defiiutiTe. While this vork lacked the elements of
originality and boldness of inception by which many of his principal
researches are characterized, it was none the less important. While
doing over again what others had done before him, he meant to do it,
and did do it, on a scale and in a way not before attempted. It was one
of the great constants of nature, and, besides, the experiment was one
surrounded by difficulties so many and so great that few possessed the
courage to undertake it with the deliberate expectation of greatly ex-
celling anything before accomplished. These things made it attractive
to Eowland.

The overthrow of the materialistic theory of heat, accompanied as
it was by the experimental proof of its real nature, namely, that it is
essentially molecular energy, laid the foundation for one of those two
great generalizations in science which will ever constitute the glory of
the nineteenth century. The mechanical equivalent of heat, the num-
ber of imits of work necessary to raise one pound of water one degree
in temperature, has, with much reason, been called the Golden ITumber
of that century. Its determination was begun by an American, Count
Eumford, and finished by Eowland nearly a hundred years later. In
principle the method of Eowland was essentially that of Eumford.
The first determination was, as we now know, in error by nearly 40
per cent; the last is probably accurate within a small fraction of 1 per
cent. Eumford began the work in the ordnance foundry of the Elector
of Bavaria at Munich, converting mechanical energy into heat by
of, a blunt boring tool in a caimon surrounded by a definite quantity
of water, the rise in temperature of which could be measured. Eowland
finished it in an establishment founded for and dedicated to the in-
crease and diffusion of knowledge, aided by all the resources and refine-
ments in measurement which a hundred years of exact science had
made possible. As the mechanical theory of heat was the germ out
of which grew the principle of the conservation of energy, an exact
determination of the relation of work and heat was necessary to a
rigorous proof of that principle, and Joule, of Manchester, to whom
belonp more of the credit for this proof than to any other one man or,
perhaps, to all others put together, experimented on the mechanical
equivalent of heat for more than forty years. He employed various
methods, finally recurring to the early method of heating water by
friction, improving on Eumford’s device by creating friction in the
water itself. Joule’s last experiments were made in 1878, ahd most
of Eowland’s work was done in the year following. It excelled that of

COMMBMOBATIVB ADDRESS

Joule, not only in the magnitude of the quantities, to be observed, but
especially in the greater attention given to the matter of thermometry.
In common with Joule and other previous investigators, he made use
of mercury thermometers, but this was only for convenience, and they
were constantly compared with an air thermometer, the results being
finally reduced to the absolute scale. By experimenting with water at
different initial temperatures he obtained slightly different values for
the mechanical equivalent of heat, thus establishing beyond question
the variability of the specific heat of water. Indeed, so carefully and
accurately was the experiment worked out that he was able to draw
the variation curve and to show the existence of a minimum value at
30 degrees C.

This elaborate and painstaking research, which is now classical, was
everywhere awarded high praise. It was published in full by the Amer-
ican Academy of Arts and Sciences with the aid of a fund originally
established by Count Eumford, and in 1881 it was crowned as a prize
essay by the Venetian Institute. Its conclusions have stood the test
of twenty years of comparison and criticism.

In the meantime, Eowland^s interest had been drawn, largely per-
haps through his association with his then colleague. Professor Hast-
ings, toward the study of light. He was an early and able o.vpoTieni
of MaxwelFs Magnetic Theory and he published important theoretical
discussions of electro-magnetic action. Eecognizing the paramount im-
portance of the spectrum as a key to the solution of problems in other
physics, he set about improving the methods by which it was produced
and studied, and was thus led into what will probably always be re-
garded as his highest scientific achievement.

At that time, the almost universally prevailing method of studying
the spectrum was by means of a prism or a train of prisms. But the
prismatic spectrum is abnormal, depending for its character largely
upon the material made use of. The normal spectnim as produced by
a grating of fine wires or a close ruling of fine lines on a plane reflect-
ing or transparent surface had been known for nearly a hundred years,
and the colors produced by scratches on polished surfaces were noted
by Eobert Boyle, more than two hundred years ago. Thomas Young
had correctly explained the phenomenon according to the undulatory
theory of light, and gratings of fine wire and, later, of rulings on glass
were used by Fraunhofer who made the first great study of the dark
lines of the solar spectrum. Imperfect as those gratings wore, Fraun-
hofer succeeded in making with them some remarkably good measures

Henet a. Eqwland

of the length of light waves, and it was everywhere admitted that for
the most precise spectrum measurements they were indispensable. In
their construction, however, there were certain mechanical dijBB.culties
which seemed for a time to be insuperable. There was no special
trouble in ruling lines as close together as need be; indeed, Robert, who
was long the most successful maker of ruled gratings, had succeeded in
putting as many as a hundred thousand in the space of a single inch.
The real difficulty was in the lack of uniformity of spacing, and on
uniformity depended the perfection and purity of the spectrum pro-
duced. Nobert jealously guarded his machine and method of ruling
gratings as a trade secret, a precaution hardly worth taking, for before
many years the best gratings in the world were made in the United
States. More than thirty years ago an amateur , astronomer, in New
York City, a lawyer by profession, Lewis M. Eutherfurd, became inter-
ested in the subject and built a ruling engine of his own design. In
this machine the motion of the plate on which the lines were ruled
was produced at first by a somewhat complicated set of levers, for which
a carefully made screw was afterwards substituted. Aided by the skill
and patience of his mechanician. Chapman, Eutherfurd continued to
improve the construction of his machine until he was able to produce
gratings on glass and on speculum metal far superior to any made in
Europe. The best of them, however, were still faulty in respect to
uniformity of spacing, and it was impossible to cover a space exceeding
two or three square inches in a satisfactory manner. When Eowland
took up the problem, he saw, as, indeed, others had seen before him,
that the dominating element of a ruling machine was the screw by
means of which the plate or cutting tool was moved along. The ruled
grating would repeat all of the irregularities of this screw and would
be good or bad just as these were few or many. The problem was,
then, to make a screw which would be practically free from periodic
and other errors, and upon this problem a vast amount of thought and
experiment had already been expended. Eowland^s solution of it was
characteristic of his genius; there were no easy advances through a
series of experiments in which success and failure mingled in varying
proportions; ^^fire and fall back” was an order which he neither gave
nor obeyed, capture by storm being more to his mind. He was by
nature a mechanician of the highest type, and he was not long in devis-
ing a method for removing the irregularities of a screw, which aston-
ished everybody by its simplicity and by the all but absolute perfection
of its results. Indeed, the very first screw made by this process ranks

COMMEMOKATIVE AdDEESS

to-day as the most perfect in the world. But such an engine as this
might only be worked up to its highest eflBlciency under the most favor-
able physical conditions, and in its installation and use the most careful
attention was given to the elimination of errors due to variation of tem-
perature, earth tremors, and other disturbances. Not content, how-
ever, with perfecting the machinery by which gratings were ruled, Row-
land proceeded to improve the form of the grating itself, making the
capital discovery of the concave grating, by means of which a large
part of the complex and otherwise troublesome optical accessories to
the diffraction spectroscope might be dispensed with. Calling to his
aid the wonderful skill of Brashear in making and polishing plane and
concave surfaces, as well as the ingenuity and patience of Schneider,
for so many years his intelligent and loyal assistant at the lathe and
workbench, he began the manufacture and distribution, all too slowly
for the anxious demands of the scientific world, of those beautifully
simple instruments of precision which have contributed so much to
the advance of physical science during the past twenty years. While
willing and anxious to give the widest possible distribution to these
gratings, thus giving everjnvhere a new impetus to optical research,
Rowland meant that the principal spoils of the victory should be his,
and to this end ho constructed a diffraction spectrometer of extra-
ordinary dimensions and began his classical researches on the Solar
Spectrum. Finding photography to be the best means of reproducing
the delicate spectral lines shown by the concave grating, he became at
once an ardent student and, shortly, a master of that art. The out-
come of this was that wonderful "Photographic Map of the Normal
Solar Spectrum,” prepared by the use of concave gratings six inches
in diameter and twenty-one and a half feet radius, which is recognized
as a standard everywhere in the world. As a natural supplement to
this he directed an elaborate investigation of absolute wave-lengths,
undertaking to give, finally, the wave-length of not only every line of
the solar spectrum, but also of the bright lines of the principal ele-
ments, and a large part of this monumental task is already completed,
mostly by Rowland's pupils and in his laboratory.

Time will not allow further expositions of the important conse-
quences of his invention of the ruling engine and the concave grating.

Indeed, the limitations to which I must submit compel the omission
of even brief mention of many interesting and valuable investigations
relating to other subjects begun and finished during these years of
activity in optical research, many of them by Rowland himself and

Hbnet a. EawLAOT)

many of them by bis pupils, working out his suggestions and con-
stantly stimulated by his enthusiasm. A list of titles of papers ema-
nating from the physical laboratory of the Johns Hopkins University
during tbia period would show somewhat of the great intellectual fertil-
ity which its director inspired, and would show, especially, his continued
interest in magnetism and electricity, leading to his important investi-
gations relating to electric units and to his appointment as one of the
United States Delegates at important International Conventions for
the better determination and definition of these units. In 1883 a com-
mittee appointed by the Electrical Congress of 1881, of which Rowland
was a member, adopted 106 centimetres as the length of the mercury
column equivalent to the absolute ohm, but this was done against his
protest, for his own measurements showed that this was too small by
about three-tenths of one per cent. His judgment was confirmed by
the Chamber of Delegates of the International Congress of 1893, of
which Rowland was himself President, and by which definitive values
were given to a system of international units.

Rowland's interest in applied science cannot be passed over, for it
was constantly showing itself, often, perhaps, unbidden, an unconscious
bursting forth of that strong engineering instinct which was born in
him, to which he often referred in familiar discourse, and which would
unquestionably have brought him great success and distinction had he
allowed it to direct the course of his life. Although everywhere looked
upon as one of the foremost exponents of pure science, his ability as an
engineer received frequent recognition in his appointment as expert
and counsel in some of the most important engineering operations in
the latter part of the century. He was an inventor, and might easily
have taken first rank as such had he chosen to devote himself to that
sort of work. During the last few years of his life he was much occu-
pied with the study of alternating electric currents and their applica-
tion to a system of rapid telegraphy of his own invention. A year ago
his system received the award of a grand prix at the Paris Exposition,
and only a few weeks after his death the daily papers published cable-
grams from Berlin announcing its complete success as tested between
Berlin and Hamburg, and also the intention of the German Postal
Department to make extensive use of it.

But behind Rowland, the profound scholar and original investigator,
the engineer, mechanician and inventor, was Rowland the man, and
any estimate of his infiuence in promoting the interests of physical
science during the last quarter of the nineteenth century would be

CoiOOlMOBATrTB AdDKESS

qxiite inadequate if not made from that point of view. Born at Hones-
dale, Pennsylvania^ on November 27, 1848, he had the misfortune, at
the age of 11 years, to lose his father by death. This loss was made
good, as far as it is possible to do so, by the loving care of mother and
sisters during the years of his boyhood and youthful manhood. Prom
his father he inherited his love for scientific study, which from the very
first seems to have dominated all of his aspirations, directing and con-
trolling most of his thoughts. His father, grandfather, and great-
grandfather were all clergymen and graduates of Yale College. His
father, who is described as one interested in chemistry and natural
philosophy, a lover of nature and a successful trout-fisherman,” had
felt, in his early youth, some of the desires and ambitions that after-
ward determined the career of his distinguished son, but yielding, no
doubt, to the influence of family tradition and desire, he followed the
lead of his ancestors. It is not unlikely, and it would not have been
unreasonable, that similar hopes were entertained in regard to the
future of young Henry, and his preparatory school work was arranged
with this in view. Before being sent away from home, however, he had
quite given himself up to chemical experiments, glass-blowing and other
similar occupations, and the members of his family were often sum-
moned by the enthusiastic boy to listen to lectures which were fully
illustrated by experiments, not always free from prospective danger.
His spare change was invested in copper wire and the like, and his first
•five-dollar bill brought him, to his infinite delight, a small galvanic
battery. The sheets of the New TorTc Olserver^ a treasured family
newspaper, he converted into a huge hot-air balloon, which, to the
astonishment of his family and friends, made a brilliant ascent and
flight, coming to rest, at last, and in flames, on the roof of a neighbor-
ing house, and resulting in the calling out of the entire fire department
•of the town. When urged by his boy friends to hide himself from
the rather threatening consequences of l^is first experiment in aero-
nautics, he courageously marched himself to the place where his balloon
had fallen, saying, ^'No! I will go and see what damage I have done.”
When a little more than sixteen years old, in the spring of 1865, he
was sent to Phillips Academy at Andover, to be fitted for entering the
academic course at Yale. His time there was given entirely to the
study of Latin and Greek, and he was in every way out of harmony
with his environment. He seems to have quickly and thoroughly ap-
preciated this fact, and his very first letter from Andover is a cry for
relief. tahe me liome!^^ is the boyish scrawl covering the last

Henet a. Kowland

page of that letter, on another of which he says, It is simply horrible
T can never get on here.” It was not that he could not learn Latin and
Greek if he was so minded, but that he had long ago become wholly
absorbed in the love of nature and in the study of nature^s laws, and
the whole situation was to his ambitious spirit most artificial and irk-
some. Time did not soften his feelings or lessen his desire to escape*
from such uncongenial surroundings, and, at his own request. Dr. Par-
rand, Principal of the Academy at Newark, New Jersey, to which city
the family had recently removed, was consulted as to, what ought to*
be done. Fortunately for everybody, his advice was that the boy ought
to be allowed to follow his bent, and, at his own suggestion, he was
sent, in the autumn of that year, to the Eensselaer Polytechnic Institute*
at Troy, where he remained five years, and from which he was graduated
as a Civil Engineer in 1870.

It is unnecessary to say that this change was joyfully welcomed by
young Eowland. At Andover the only opportunity that had offered
for the exercise of his skill as a mechanic was in the construction of a,
somewhat complicated device by means of which he outwitted some of
his schoolmates in an early attempt to haze him and in this he took
no little pride. At Troy he gave loose rein to his ardent desires, and
his career in science may almost be said to begin with his entraiice upon
his work there and before he was seventeen years old.

He made immediate use of the opportunities afforded in Troy and
its neighborhood for the examination of machinery and manufacturing-
processes, and one of his earliest letters to his friends contained a clear'
and detailed description of the operation of making railroad iron, the*
rolls, shears, saws, and other special machines being represented in
uncommonly well executed pen drawings. One can easily see in this
letter a full confirmation of a statement that he occasionally made later
in life, namely, that he had never seen a machine, however complicated
it might be, whose working he could not at once comprehend. In
another letter, written within a few weeks of his arrival in Troy, he-
shows in a remarkable way his power of going to the root of things
which even at that early age was sufficiently in evidence to mark him
for future distinction as a natural philosopher. On the river he saw
two boats equipped with steam pumps, engaged in trying to raise a
half -sunken canal boat by pumping the water out of it. He described
engines, pumps, etc., in much detail, and adds, But there was one
thing that I did not like about it; they had the end of their discharge
pipe about ten feet above the water so that they had to overcome a

COMMEMOEATIVB AdDBESS

pressure of about live pounds to the square inch to raise the water so
high, and yet they let it go after they got it there, whereas if they had
attached a pipe to the end of the discharge pipe and let it hang down
into the water, the pressure of water on that pipe would just have
balanced the live pounds to the square inch in the other, so that they
could have used larger pumps with the same engines and thus have got
more water out in a given time."

The facilities for learning physics, in his day, at the Eensselaer Poly-
technic Institute were none of the best, a fact which is made the subject
of keen criticism in his home correspondence, but he made the most of
whatever was available and created opportunity where it was lacldng.
The use of a turning lathe and a few tools being allowed, he spent all
of his leisure in designing and constructing physical apparatus of var-
ious kinds with which he experimented continually. All of his spare
money goes into this and he is always wishing he had more. While he
pays without grumbling his share of the expense of a class supper, he
cannot help declaring that it is an awful price for one night’s pleas-
ure; why, it would buy another galvanic battery." During these early
years his pastime was the study of magnetism and electricity, and his
lack of money for the purchase of insulated wire for electro-magnetic
apparatus led him to the invention of a method of winding naked
copper wire, which was later patented by some one else and made
much of. Within six months of his entering the Institute he had made
a delicate balance, a galvanometer, and an electrometer, besides a small
induction coil and several minor pieces. A few weeks later he an-
noiinces the finishing of a Euhmkorff coil of considerable power, a
source of much delight to him and to his friends. In December, 18GC,
he began the construction of a small but elaborately designed steam
engine which ran perfectly when completed and furnished power for
his experiments. A year later he is full of enthusiasm over an investi-
gation which he wishes to xindertake to explain the production ot
electricity when water comes in contact with red-hot iron, which h(‘
attributes to the decomposition of a part of the water. Along with all
of this and much more he maintains a good standing in his regular work
in the Institute, in some of which he is naturally the leader. He occa-
sionally writes:— I am head of my class in mathematics," — or ^^I lead
the class in Natural Philosophy," but official records show that he was
now and then ^^conditioned" in subjects in which he had no special
interest. As early as 1808, before his twentieth birthday, he decided
that he must devote his life to science. While not doubting his ability

Henet a, Eowlaio)

make an excellent engineer as he declares, he decides against
engineering, saying, ^^Yon know that from a child I have been ex-
tremely fond of experiment; this liking instead of decreasing has gradu-
ally grown upon me until it has become a part of my nature, and it
would be folly for me to attempt to give it up; and I don^t see any
reason why I should wish it, unless it be avarice, for I never expect
to be a rich man. I intend to devote myself hereafter to science. If
she gives me wealth, I will receive it as coming from a friend, but if
not, I will not murmur/^

He realized that his opportunity for the pursuit of science was in
becoming a teacher, but no opening in this direction presenting itself
he spent the first year after graduation in the field as a civU engineer.
This was followed by a not very inspiring experience as instructor in
natural science in a Western college, where he acquired, however,
experience and useful discipline.

In the spring of 1872 he returned to Troy as instructor in physics,
on a salary the amount of which he made conditional on the purchase
by the Institute of a certain number of hundreds of dollars^ worth of
physical apparatus. If they failed in this, as afterward happened, his
pay was to be greater, and he strictly held them to the contract. His
three years at Troy as instructor and assistant professor were busy,
fruitful years. In addition to his regular work he did an enormous
amount of study, purchasing for that purpose the most recent and most
advanced books on mathematics and physics. He built his electro-
dynamometer and carried out his first great research. As already
stated, this quickly brought him reputation in Europe and what he
prized quite as highly, the personal friendship of Maxwell, whose ardent
admirer and champion he remained to the end of his life. In April,
1875, he wrote, " It will not be very long before my reputation reaches
this country,^^ and he hoped that this would bring hiTYi opportunity to
devote more of his time and energy to original research.

This opportunity for which he so much longed was nearer at hand
than he imagined. Among the members of the Visiting Board at the
West Point Military Academy in June, 1875, was one to whom had
come the splendid conception of what was to be at once a revelation and
a revolution in methods of higher education. In selecting the first
faculty for an institution of learning which, within a single decade, was
to set the pace for real university work in America, and whose influence
was to be felt in every school and college of the land before the end of
the first quarter of a century. Dr. Gilman was guided by an instinct

OoiUIEUOJlAXiyE Addsess

which more than, all else msured the success of the new enterprise.
A few words about Rowland from Professor Michie, of the Military
Academy, led to his being called to West Point by telegraph, and on
the btiTilffl of the Hudson these two walked and tallced, “ he telling me,”
Dr. Gilman has said, “his dreams for science and I telling him my
dreams for higher education.” Rowland, with characteristic frank-
ness, writes of this interview, “ Professor Gilman was very much
pleased with me,” which, indeed, was the simple truth. The engage-
ment was quickly made. Rowland was sent to Europe to study labor-
atories and purchase apparatus, and the rest is history, already told and
everywhere known.

Rowland’s personality was in many respects remarkable. Tall, erect
and lithe in figure, fond of athletic sports, there was upon his face a
certain look of severity which was, in a way, an index of the exacting
standard he set for himself and others. It did not conceal, however,
what was, after all, his most striking characteristic, namely, a perfectly
frank, open and simple straightforwardness in thought, in speech and
in action. His love of truth held him in supreme control, and, like
Galileo, he had no patience with those who try to make things appear
otherwise than as they actually are. His criticisms of the work of
others were keen and merciless, and sometimes there remained a sting
of which he himself had not the slightest suspicion. “I would not
have done it for the world,” he once said to mo after being told that
his pitiless criticism of a scientific paper had wo\mded the feelings of
its author. As a matter of fact he was warm-hearted and generous, and
hie occasionally seeming otherwise was due to the complete separation,
in his own mind, of the product and the personality of the airthor. Ho
possessed that rare power, habit in his case, of seeing himself, not as
others see him, but as he saw others. He looked at himself and his own
work exactly as if he had been another person, and this gave rise to a
frankness of expression regarding his own performance which some-
times impres’sed strangers unpleasantly, but which, to his friends, was
one of his most charming qualities. Much of his success as an investi-
gator was due to a firm confidence in his own powers, and in the unerring
course of the logic of science which inspired him to cling tenaciously
to an idea when once he had given it a place in his mind. At a meeting
of the national Academy of Science in the early days of our knowledge
of electric generators, he read a paper relating to the fundamental
principles of the dynamo. A gentleman who had had large experience
with the practical working of dynamos listened to the paper, and at the

Henry A. Eqwland

end said to the Academy that nnfortunately practice directly contra-
dicted Professor Bowland^s theory, to which instantly replied Bowland,

So much the worse for the practice,” which, indeed, turned out to be
the case.

Like all men of real genius, he had phenomenal capacity for concen-
tration of thought and effort. Of this, one who was long and intimately
associated with him remarks, I can remember cases when he appeared
as ii drugged from mere inability to recall his mind from the pursuit
of all-absorbing problems, and he had a triumphant joy in intellectual
achievement such, as we would look for in other men only from the
gratification of an elemental passion.” So completely consumed was
he by fires of his own kindling that he often failed to give due attention
to the work of others, and some of his public utterances give evidence
of this curious neglect of the historic side of his subject.

As a teacher his position was quite unique. Unfit for the ordinary
routine work of the class room he taught as more men ought to teach,
by example rather than by precept. Says one of his most eminent
pupils, Even of the more advanced students only those who were able
to brook severe and searching criticism reaped the full benefit of being
under him, but he contributed that which, in a University, is above all
teaching of routine, the spectacle of scientific work thoroughly done
and the example of a lofty ideal.”

Eetuming home about twenty years ago after an expatriation of
several years, and wishing to put myself in touch with the development
of methods of instruction in physics and especially in the equipment of
physical laboratories, I visited Eowland very soon after, as it happened,
the making of his first successful negative of the solar spectrum. That
he was completely absorbed in his success was quite evident, but he also
seemed anxious to give me such information as I sought. I questioned
hira^as to the number of men who were to work in his laboratory, and
although the college year had already begun he appeared to be unable
to give even an approximate answer. ^^And what will you do witli
them?” I said. "Do with them?” he replied, raising the still drip-
ping negative so as to get a better light through its delicate tracings,
"Do with them ? — I shall neglect them” The whole situation was in-
tensely characteristic, revealing him as one to whom the work of a drill -
master was impossible, but ready to lead those who would be led and
could follow. To be neglected by Eowland was often, indeed, more
stimulating and inspiring than the closest personal supervision of men
lacking his genius and magnetic fervor.

COMMEMOEATIYE AbDRESS

In the fulness of his powers, recognized as Americans greatest physi-
cist, and one of a very small group of the world’s most eminent, he died
on April 16, 1901, from a disease the relentless progress of which he had
realized for several years and opposed with a splendid but quiet courage.

It was Eowland’s good fortune to receive recognition during his life
in the bestowal of degrees by higher institutions of learning; in elec-
tion to membership in nearly all scientific societies worthy of note in
Europe and America; in being made the recipient of medals of honor
awarded by those societies; and in the generously expressed words of
his distinguished contemporaries. It will be many years, however, be-
fore full measure can be had of his influence in promoting the interests
of physical science, for with his own brilliant career, sufiicient of itself
to excite our profound admiration, must be considered that of a host
of other, younger, men who lighted their torches at his flame and who
will reflect honor upon him whose loss they now mourn by passing on
something of his unquenchable enthusiasm, something of his high
regard for pure intellectuality, something of his love of truth and his
sweetness of character and disposition.

SCIENTIFIC PAPERS

PART 1

EARLY PAPERS

THE VORTEX PROBLEM

iScientijlc American^ XXIJy 808, 1865]

Messrs. Editors: — ^In. a late number of your paper an inquiry waB
made why a vortex was formed over the orifice of an outlet ‘ pipe; as,
for instance, in a bath tub, when the water is running out. If the
water be first started, the explanation will be on the same principle
that a ball and string will, if started, wind itself up upon the hand; the
ball being attached to the string will, as the string winds up, get nearer
the hand, and, conseqiiently, will have less far to go to make one revo-
lution, and thus the momentum, though perhaps not great enough t6
carry it around in the great circle, is still sufl&cient to make it revolve
in the smaller one.

Therefore, as the string is continually winding up, and tho ball con-
tinually nearing the hand, it will, if the resistance of the air is not too
great, continue to revolve until the string is wound up. How, in the
case of tho water, eacli particle of it will represent the ball, the force
of tho water rushing toward the outlet will be the string, and, the water
mmiing oiit, and thus causing the particles to come nearer tho center
at every revolution, will represent the winding-up process. Thus, we
see this case is analogous to the preceding, and the same reason that
will apply to one will apply to the other. I suppose that some slight
motion existing among tho particles of the water, united to the motion
produced by the outlet, causes tho vortex to begin, and, once begun, it
will continue until tho water is exhausted.

Such motion could cither previously exist, or noight be produced by
the form’ of the vessel, which would cause the water, in running to
the otitlet, to assiime a certain direction.

H. A. R.

Troy, N', Y,^ Oaioberj 1805.

J[Tn tbo original article thifl reads “outlet of an orlOce,’* an obvious misprint,]

9 [In the original article this word is “power,” an obvious misprint.]

PADTE’S ELECTEO-MAGNBTIO ESTGIirE

{ScUfitiJic American^ XXV^ 21, 1871]

To the Editor of the Scientific American:

Having noticed several articles in your paper mth reference to
Paine’s electro-magnetic maclime^ I believe I cannot do better than
describe a visit which I paid it about three months ago.

Entering the office in company with a friend, at about twelve o’clock
one day, I was told that the machine was not running then, but would
be in operation at one. Proceeding there alone, at about that time, I
was, after the formality of sending up my name, conducted by a small
boy, through numerous by-ways and passages, to the second story of a
back building, where I was met by the illustrious inventor and a few
select friends. Mr. Paine began by showing the small model machines,
which he set in motion by a battery of four cups, of about a gallon
capacity each. These models revolved very well, but apparently with no
power, for they could be stopped easily. I then began to reason with
him on the absurdity of his position, and adduced in my support the
experiments of Joule, Mayer, Earaday and others. He, evidently, had
no very high opinion of these, and pronounced the conservation of force
an old fashioned idea, which had been overthrown in these enlightened
days by his " experiments,’^ though what the latter were I have never
determined.

After conversing some time, to no purpose, he prepared to over-
throw me and my authority at one blow, by an exhibition of The
Machine. This was standing in front of a chimney, on one side of the
room, with the axis of its wheels parallel to the wall. The wheel to
which the magnets were attached was, unlike the models, inclosed in a
cast iron case, which enveloped it closely above, but spread out into a
rectangular base below. The latter rested directly on the floor. Th(‘
axis of the wheel projected on each side, and, to one end, a pulley was
attached, and to the other, the brake for operating the magnets. The
machine had the general appearance of a fan blower with an enlarged
pulley. The battery was attached to two binding screws, fixed to a

Paine's Eleotbo^-Magnetio Engine 25

standard on the chimney, and the current was supposed to pass from
these, along wires, to the break piece, and thence to the magnets. A
belt on the pulley connected with a shaft overhead, whence another belt
proceeded to the pulley of a small circular saw.

As soon as the connection was made with the battery, the whole
apparatus began to move, and soon the saw attained great velocity,
shaking the building with violence. The latter effect was caused by a
heavy fly wheel on the saw arbor, which probably was not well balanced.
When well in motion, boards were applied and sawed with the greatest
ease. To show the excess of power, they were sometimes placed on
edge and passed over the saw, so as wholly to envelop it, and the cut
made from end to end, without the velocity being at all diminished.
On throwing off the belt from the saw, the machine still proceeded at
the same velocity, with entire indifference to external resistance. On
mentioning this to Mr. Paine, he informed me that when the saw was
attached, and the resistance gi‘eater, the increased pull on the magnets
brought them nearer together, by bending the heavy iron frame; and,
as magnetic attraction varies inversely as the square of the distance, it
only required a small change of distance to account for the increased
power. I clearly indicated that I was skeptical on this point, and sug-
gested that it would also work without variation if the power pro-
ceeded from some well governed steam engine in the neighborhood*
On this he intimated that, if I were not careful, a force might proceed
from his body which would act in conjiinction with gravitation in
causing me to be projected through the window, and strike with vio-
lence on the ground below.

The exhibition being over, on going down stairs in company with the
rest, I tried the door of the room below, but found it locked, and the
windows covered with papers. I desired to get in, but was met with
the assurance that the room was rented by a man who was tlicn absent.

This, 1 believe, is the last visit paid by an outsider to this wondcjrM
invention. I have boon there several times since, but there has been
no admittance to me, or to any one else. I have since been to the
owner of the building, and find that Mr. Paine rents the room to which
I sought admittancjo, and also rents power in that same room, which is
directly below that containing his machine. The engine from which
the power comes generally stops work at twelve and starts again at
one, but sometimes works all day.

My visits there have established the following facts: First, That
my friend and I were denied admittance at twelve o'clock, but wore

Bjinky a. Eowlaitd

invited to come at one. Second^ That the shaft in the room below does
not revolve between the hours of twelve and one. Third, That the
room below, containing power, was rented by Mr. Paine, but that he
kept it carefully locked^ and misguided me as to the tenant. Fourth,
That the working parts are concealed in an unnecessarily strong case,
wen adapted to the concealment of another source of power. Fifth,
That part of the apparatus is attached to the wall, so that the machine
must always occupy the same position on the floor. Sixth, That the
models have not a power proportionate to their size. Seventh, That
the machine runs at the same velocity, whether producing one horse
power or a fraction of a horse power, and this without a governor.

These are the facts of the case. Where the power of the machine
comes from I am unable to say. Is there some secret connection be-
tween this machine and the shaft below, and does the battery serve
only to make this connection? Or does the battery, when applied,
connect the apparatus with a larger battery? I leave these questions
to others; but, unless the reasoning and experiments of a host of our
greatest men be false, and unless the greatest development of modern
science be overthrown, this machine cannot but derive its power from
some extraneous source.

In a late communication to your paper, Mr. Paine sets himself ixp
as the peer of Faraday, Tyndall and others, and gives as the reason,
his long devotion to science. He evidently does not consider that to
be ranked with such men requires something more than devotion; it
requires brains; brains to discriminate between true science and quack-
ish nonsense; brains to discover and originate. And pray what fact,
among the thousands of science, does Mr. Paine pretend to have proved
beyond doubt? Let him. answer. As to Mr. Paine’s sciemte,’^ I
assert that it is a tissue of error and ignorance, from beginning to end.
Even his vaunted invention of metallic foil, wherewith to envelop his
magnets or wire, can operate in no other manner than to the detriineni,
of his machine, as any such metallic coating lengthens the domagnoti-
zation, which is the very thing to be guarded against. This is duo to
an induced current, which forms in the coating, and, being in the sam(^
direction as the primary current, operates in the same Tnauncr to keep
up the magnetism. His reason for the machine’s keeping at the same
velocity also shows great ignorance of the subject. In the first placo,
the law of magnetic force, under these circumstances, is statf»f1 on ti roly
wrong. For this case, the true law is complex, hnt most lU'arly ap-
proaches to that of inversely as the distance, instead of as the square of

Paine’s Eleotko-Magnetio Engine 27

the distance. (See Joule, and also Tyndall, in the London, Edinburgh
and Dublin Philosophical Magazine fox 1850.) And, in the second
place, approach of the poles would not necessarily increase the effi-
ciency; in this kind of machine there is a distance of maximnm effi-
ciency; and if the magnets revolve at a distance greater than this, the
attraction becomes too small; and if at a less distance, the times of
magnetizing and demagnetizing the magnets become too great, and the
machine goes too slowly. The distance in this machine is, undoubtedly,
within the limit, for Mr. Paine prides himself npon its smallness, and
so further reduction, could it take place, can act in no other manner
than the opposite of that claimed. But it is my opinion that all the
force brought to boar on the magnets could not move them one two-
hundredth of an inch, when attached to such a frame.

As to Mr. Panic’s disregard for the conservation of force, I have
little to say. His assertions are made directly in the face of this
principle, and yet he has never adduced one experiment, or even a plaus-
ible reason, to prove what he says. He takes you into a building where
shafts are revolving by the vulgar power of steam, and directs you to
look while he evokes power from nothing. You must not touch any-
thing; you must not enter the room below; you must not be there while
the engine next door is at rest; but you must simply look, and by that
renowned maxim of fools, that seeing is believing,” you must believe
that the whole structure of science has fallen, and that above its ruins
nothing remains but Mr. Paine and his wonderful electro-magnetic
machine.

Henry A. Eowland, O.B.

Ncwarlx ^ iV. * T .

ILL1JSTIL4.TI0N' OP RESONAITCES A'N'T) AOTIOirS OP A
SIMILAR NATURE

IToumal of the FramMin Inatitute, XOIV, 276-378, 1872)

At the present day, when scientific education is teginning to take
its proper place in the public estimation, anything which can help
toward imparting a clear idea of any physical phenomenon becomes im-
portant. There are a number of these phenomena, of which resonance
is one, which play quite an important part in nature, but which as yet
have not been illustrated with sufdcient clearness in the lecture-room.
Among these are the following : A person carrying water may so time
his steps as to produce waves which shall rise and fall in unison with
the motion of his bodyj soldiers in crossing a bridge must not keep
step, or they may transmit such a vibration to it as to break it down;
window-panes are sometimes cracked by sounding a powerful organ-
pipe to which they can vibrate; a tuning-fork will respond to another of
equal pitch sounded near it; and others will readily suggest themselves
to the reader. In all these cases we have two bodies which can vibrate
in equal times, connected together either directly or by some medium
which transmits the motion from one to the other. We can, then,
readily reproduce the circumstances in the lecture-room.

The vibrating bodies which I have found most convenient are pendu-
lums; they are easily made, are seen well at a distance, and their time
of vibration can be easily and quickly regulated. The apparatus can
be prepared in the following manner: Fix a board, about a foot long,
in a horizontal position; suspend a piece of small stiff wire, of equal
length, beneath its edge, parallel to it, and an inch or two distant, by
means of threads. To one end of the board suspend a pendulum, con-
sisting of a thread about ten or twenty inches long, to which is attached
a ball weighing two or three ounces ; join the thread of this pendulum
to the horizontal wire by taking a turn of it around the wire, so that
when the pendulum oscillates, it causes the wire to move back and
forth in unison with it. To complete the apparatus, prepare a number
of small pendulums by suspending bullets to threads, and let them have
small hooks of wive to hang by.

Illusteation of Ebsonanoes

Having then set the heavy pendnlnm in motion, hang some of the
light ones on the horizontal wire, and note the result : those which are
shorter or longer than the heavy one will not he affected, hut if any of
them are nearly of the same length, they will begin to vibrate to a
small extent, but will soon come to rest, after which they will com-
mence again, hut stop as before; hut if any one happens to be of exactly
the proper length, its motion will soon become very great, and im-
mensely surpass in amplitude that of the heavy one, although the motion
is derived from it. Of course the heavy pendulum must he retarded in
giving motion to the light one, hut it is hardly perceptible when there is
great difference in the weight- In the same manner a tuning-fork will
undoubtedly come to rest sooner when producing resonance than when
vibrating freely. To show this retardation more clearly, suspend two
pendulums, equal in weight and length, to the edge of a horizontal
hoard, and connect their two threads together by a horizontal thread
tied to each at a point an inch or two from the top, and drawn so tight
as to pull each of the pendulums a little out of plumb- On starting one
of these penduiums the other will gradually move, and finally absorb
all the motion from the first, and bring it entirely to rest; the action
will then begin anew, and the motion will be entirely given hack to the
first ball- This experiment differs from that of resonance, inasmuch
as in the case of the pendulums all the motion of the first hall is finally
stored up in the second; but in the case of resonance the confined air
is constantly giving out its motion to the atmosphoxo in waves of sound.
To imitate this to some extent wc must attach a rather largo piece of
paper to the second pendulum, so that it will meet with resistance, and
then both halls will come to rest sooner than otherwise. If one of the
balls is only two or three times heavier than the other, they will then
also interchange motions; hut when the heavy ball has the motion,
the arc of its vibration will not be so groat as that of the other when
it vibrates.

To illustrate the use of Helmholtz resonance globes, or Koenig^s
apparatus for the analysis of sounds, we can enlarge and modify the
first apparatus somewhat. Make the board six or eight foot long, and
suspend at one end four or five of the heavy pendulums, aud at the
other the same number of light ones, each of which corresponds in time
of vibration with one of the heavy ones. On now causing any of the
heavy pendulums to vibrate, as Wo. 3, we shall meet with no response
from any of tho light ones except No. 7, If Nos. 1, 2 and 4 are sot
going at one time, the wire A will he drawn hither and thither by the

Hbotlt a. Howland

conflictmg pulls with no seeming regularity, but each of the balls 6,
6 and 8 wlII pick out from the confused motion the ribration due to
itself, and will move in unison, but !N‘o. 7 will remain <iuiet. The short
pendulums always produce the effect sooner than the long ones. To
remedy this to some extent it is well to bend the wire A into the shape
shown in the figure. It is not well to make the pendulum more than
twenty inches long, if a quick response is wished. There seems to be
no limit to the number of pendulums which can be used or the distance
to which the effect can be transmitted, though it is more decided when
there are but few pendulums and they are near together. It may some-
times be more convenient to suspend the pendulums from a wire.

tightly stretched, than from a board. To make the balls visible at a
distance, it may be well in some cases to naake them of polished steel,
and illuminate them by a beam from the electric lamp.

These experiments have many advantages which recommend them to
teachers; they can be performed without purchased apparatus, and
can be made to illustrate resonance and the kindred phenomena in all
their details. Indeed, any one will be well repaid for spending an hour
in performing them, simply for their own beauty.

ON THE AimOEAL SPBCTETTM

(America?i Journal of Soieuce TS], T, S30, 1878]

A letter from Henry A. Eowland, at present Instructor in Physics in
the Eensselaer Polytechnic Institute at Troy, inf onus us that he
observed the line of wave-length 431 in the auroral spectrum of last
October. He says: “The observations were made with an ordinary
chemical spectroscope of one prism, in which the scale was read by
means of a lamp. GrSat care was taken in the readings, and after com-
pleting them the spectroscope was set aside until morning, when the
readings were taken on the lines of comparison without altering the
instrument in any way or even regulating the slit. The wave-lengths
of the known lines were taken from Watts’s * Index of Spectra,’ but as
bo does not give the wave-lengths of lines in the flame spectrum I am
not quite certain that they are correct.” On the scale of his instru-
ment, Li a was at 13.6®, Ca a 21®, Naa2'J'.6®, Oa ^9 36®, Cay96.6®, and
K ;? 1 1 0®. The aurora lines were as foEows:

Soalo-roading.

Wavo-longths.

628.3

36.6

664.3

426

“ The wave-lengths of the auroral lines were obtained by graphical
interpolation on such a large scale as to introduce Ettle or no error.”

PART II

MAGNETISM AND ELECTRICITY

OIT MAGNETIC PERMEABILITY/ AND THE MAXIMUM OF
MAGNETISM OF IRON, STEEL, AND NICKEL

^Philosophical MafjaslneW, XTjVI, 140-ir»i>, IHTiij

Moro than three yoara ago 1 eomnieneod the series o£ experiiucnts
the results ol which I now publish for tlie iirst time. Many of the
facts which I now give were obtained then; but, for satisfacdory r<)asons,
they were not published at that time. Tlui investigations were eoin-
jnenccd witli a view to determine the distribution, of ;nmgnolism on
iron bars and steel magnets; but it was soon found that little could be
done without new experiments on the .magnetic i)erineal)ility of sub-
stances.

Few observations liave been made as y(it for determining the mag-
netic permeability of iron, and noms J beli(wo, of nickel and cobalt, in
absolute measure. Th(‘ snl)je(d; is importani., b(u*aiisc‘ in all theories of
induced magnetism a quantity is introduced (hqamding upon tins tnag-
ncdic properties of the suhstanc(‘, and without a knowledges of which
the prohhmi is of little lait iheoristical intensst; this quantity lias
always been treated as a <*onstant, alihougli the <‘.\p(‘rimenls on the
maximum of magnetism show that it is a variable*. II(»wevt‘r, tlie form
of the function has msvew h(*(»ii dcden’iniinsd, (‘X(*ept so far as we may
deduce it from Uie equation of Jliillor,

whi(,di, as will ho shown, hsads to wrong resuHs. ^Phe quani.ities used
by different persons are as follows: —

«, ISreumann’s co(3lTlcient, ov .magnetie susc(‘i)iil>iliiy (Tliomson).
h PoissoTi’s (soellici(‘nt.

/A, coefficient of magiiolizalion (Maxwell), or magn(‘li(* ixurnnsability
(Thomson).

introduced for eonvcnicmce in lln* following ]>a])i*r.

^The word “pormoaMlity has boon ]»n)poBO(l by Thomfion, and huH tbn Hame
mcaninc: m “conductivity” as used by Faraday (* I»aporfl on FI«ctri(‘Ity and
ism,’ Thomson, p. 484; Maxwoirs * Klectrioity and Ma^^netlsm,’ vol. U, p. 51.)

Hentry a. Eqwland

The lelatioRS of these (quantities are given by the following equa-
tions: —

Z— . A— 4 :r

4:7tK-h3 At + S A + Stt’

/I — 1 ZJc X — 4? ?

^ 47r 47r(^l— "" IBtt* ’

1 + 2/ff ^ ^ ^

M=-xz:^=4^«+i = Ar-

471

The first determination of the value of any of these quantities was
made by Thal6n. But more important experiments have been made
by Weber, Von Quintus leilius, and more recently by M. Eeicke and
Dr. A. Stoletow.® The first three of these in their experiments used
long cylindrical rods, or ellipsoids of great length; the last, who has
made by far the most important experiments on this subject, has used
an iron ring. The method of the ring was first used by Dr. Stoletow
in September, 1871; but more than eight months before that, in Jan-
uary, 1871, I had used the same method, but with different apparatus,
to measure the magnetism. He plots a curve showing the variation of
#c; but he plots it with reference to B as abscissa instead of B and
thus fails to determine the law. His method of experiment is much
more complicated than mine, so that he could only obtain results for
one ring; while by my method I have experimented on about a dozen
rings and on numerous bars, so that I believe I have been eiuilfiod to
find the true form of the function according to which varies with the
magnetism of the bar or the magnetizing-force.

Many experiments have been made on the magnetism of iron without,
giving the results in absolute measure. Among these arc tlu^ experi-
ments of Miillcr, Joule, Lenz and Jacobi, Dub, and others. The cw'-
periments have been made by the attraction of cloctromagnots, by tlio
deflection of a compass-nocdlc, or, in one case, by measuring tlio in-
duced current in a helix extending the whole length of the bar. By
the last two methods the change in the duirUndioii of inagnciisin ov(‘r
the har when the magnotisin of the bar varies is flisrogard(‘(l, if indec^d
it was thought of at all: even in a reecnit inemoir of M. Oazin “ wo lia,V(‘
the statement made that tlio position of the polos is indepoiHhuii of ilio
strength of the current. He does not give the experiment from wlii(di
he deduces this result. Now it is very easy to show, from iho formula

* Phil. Mag., January, 1873.

^Annalesde CMmie et (fe T/fysiqne^ Feb., 1873, p. 171.

Magnetic Peemeabiiity op Irok, Steel a^3d Niokel 31

of Green for the clistribxition of magnetism: on a bur-niagiiot combined
with the known variation of that this can only be true for short and
thick bars; and it has also been remarked by Thojiison that this should
be the case.* An experiment made in 1870 places this l)oyon(i doubt.
A small iron wire (No. IG), 8 inches long, was wound witli two lay(u*s of
fine insulated wire; a small hard steel magnet i inch long suspended by
a hbre of silk xvas rendered entirely astatic by a large magnet placed
about 2 feet distant; the wire electromagnet was then ])laciod near it,
so that the needle hung 1|- inch from it and about 2> inches liack from
the end. On now exciting the magnet with a wc^ak current, the needlo
took u|) a cH*rtain definite position, indicating the tlivocdion of the line
of force at that point. When the current was very nnicli intn*(usod, the
needle instantly moved into a position more nearly pjirallel to ilie
magnet, thus showing that the magnetism was now distribiiltui more
nearly at the ends than before. This show's that nearly all ih(>^ exi)eri-
ments hitherlo made on bar-nmgnots contain an error; hut, owing i.o
its small amount, we can a<*ccpt the results as ap])roxiiuat(^ly true.

I believe mine are the first experiments Jiitherto made on Ihis subject
in which tlie results are (‘xpressed and the reasoning (tarried out in thi^
language of Faraday's theory of lines of inagindie I'orta'; and the iiiiliiy
of tliis metliod of tlunking is shown in the method of (experimenting
adoptcMl for moasuriug magnetism in absolute nioasur(‘, for wliich f
claim that it is the simplest and most ac^curaie of any yet devised.
AVhetlier Faraday's theory is eorrect or not, it is w(‘Il known (hat its
use will give correct n^suHs; at lln^ liini^ ilu^ tendency of Ihe

most advanced thongbt is lowanl the iheory and indeed it has l)e(*n
pointed out by Sir William Thomson that it follows, from dynamical
reasoning iijion the magnetic I'otation of tbo plain' of ixdari/ation of
light, that tll(^ nu'diniu in whi(di this takes place' must itself be in
rotation, the axis of rotation being in the direedion, of the liin's < 11 *
■foree.® Some suhstances must of ruuwsil.y l)e inor<‘ capable of assum-
ing this rotary motion tlian others; nnd Ik'ikm* aris<'s the notion of
magnetie '^(conductivity " and "iienneability."

Thomson has pointcul out several analogies wdii(di may he used in
calculating the distrihution and direeddon of the lim*s of fon'c' iimh'r
various eirenmstaneos. He has shown tluit the inatheumt icad (r<*atmont

4 Papers on Electricity and Maj^notisni, p. .503.

fi“On Action at a Distance,” Miuwell, *Natur(5,’ Pel). 37 unci ManUi 0 tind ID, lH7a.

^Thomson’s ‘Papers on Electricity and Ma^i:netlBini,’ p. 411), notc^; and Maxwell’s
‘Treatise on Electricity and Magnetism,’ vol. ii, chap. xxi.

Henry A. Rowland

of magnetism is the same as that of the flow of heat in a solid, as the
static induction of electricity, and as the flow of a frictionless incom-
pressible liquid through a porous solid. It is evident that to these
analogies we may add that of the conduction of electricity.' We readily
see that the reason of the treatment being the same in each case is that
the elementary law of each is similar to Ohm's law. Mr. Webb " has
shown that this law is useful in electrostatics; and I hope, in a sequel
to this paper, to apply it to the distribution of magnetism: I give two
equations derived in this way further on.

The absolute units to which I have reduced my results are those in
which the metre, gramme, and second are the fundamental units. The
unit of magnetizing-force of helix I have taken as that of one turn
of wire carrying the unit current per metre of length of helix, and is
4:7r times the unit magnetic field. This is convenient in practice, and
also because in the mathematical solution of problems in electrodynam-
ics the magnetizing-force of a solenoid naturally comes out in this unit-
The magnetizing-force of any helix is reduced to this unit by multiply-
ing the strength of current in absolute units by the number of coils in
the helix per metre of length. These remarks apply only to endless
solenoids, and to those which are very long compared with their diam-
eter. The unit of number of lines of force I have taken as the number
in one square metre of a unit field measured perpendicular to their
direction. As my data for reducing my results to these units, I have
taken the horizontal force of the earth’s magnetism at Troy as 1-64:1,
and the total force as 6-2'?'.

The total force, which will most seriously affect my results, is well
loiown to he nearly constant at any one place for long periods of time.

From the analogy of a magnet to a voltaic battery immersed in water
I have obtained the following, on the assumption that /ji is constant,
and that the resistance to the lines of force passing out into the medium
is the same at every point of the bar.

Let R = resistance to lines of force of one inetre of length of bar.
J2' = resistance of medium along 1 metre of length of bar.

(?' = lines of force in bar at any point.

lines of force passing from bar along small distance J.
e =base of Napierian system of logarithms,
a: = distance from one end of helix.

Maxwell’s ‘Treatise on Electricity and Magnetism,’ arts. 348, 344 and 245.

8 “ Application of Ohm’s Law to Problems in Electrostatics,” Phil. Mag. S. 4, vol.
zxxv, p. 835 (1868).

Henbt a. Eowland

interior of the ring-solenoid, the magnetic field at that point will, as is
well blown, he

and at a point within an infinitely long solenoid

47rm.

If the solenoid contain any magnetic material, the field will be for
the ring

and for the infinite solenoid

4i7tnin.

Therefore the numher of lines of force in the whole section of a ring-
magnet of circular section will he, if o is the mean radius of the ring,

Q=AM'i/i , y ^ dai= ;

%/ — jB d *“ (C

or, since nf == 2 Tt an and M ~ we have, hy developing,

+ + ^|*+ . . (6)

For the in fini te electromagnet we ha-ve in the same way for a circular
section,

Q' = 47r Jf/x(jri2») (7)

When the section of the ring is thin, equation (6) becomes the same
as equation (7), and either of them will give

which is the same as equation (5).

In all the rings used the last parenthesis of (6) is so nearly unity
that the difference has in most cases been neglected, the slightest change
in the quality of the iron producing many times more effect on the
peimeability than this. Whenever the difference amounted to more
than it was not rejected.

The apparatus used to measure Q' was based upon the fact discovered
by Paraday, that the current induced in a closed circuit is proportional
to the numher of lines of force cut by the wire, and that the deflection
of the galvanometer-needle is also, for small deflections, proportional
to that numher. In the experiments of 1S70-71 an ordinary astatic
galvanometer was used; but in those made this year a galvanometer was

Magn'Etio Peemeability op Iron, Steel and ITickel 41

specially constructed for the purpose. It was on the principle of Thom-
son's reflecting instrument, but was modified to suit the case by increas-
ing the size of the mirror to § of an inch, by adding an astatic needle
just above the coil withoul adding another coil, by loading the needle
to make it vibrate slowly, and, lastly, hy looking at the reflected image
of the scale through a telescope instead of observing the reflection oE a
lamp on the scale. The galvanometer rested on a firm bracket attaclied
to the wall of the laboratory near its foundation. In most of tho ex-
periinents the needle made about five single vibrations per mimite.
The astatic noodle was added to prevent any external magnetic force
from deflecting the noodle; and directive force was given by the magnet
above. Each division of the scale was “ 075 inch long; and the extrem-
ities of the scale were reached by a deflection of 7° in the needle from 0.
The scale was hent to a radius of 4 feet, and was 3 feet from the instru-
ment. At first a correction was made for the resistance of the air, &c.;
but it was afterwards found by experiment that the correction was very
exactly proportional to tho deflection, and hence could bo disponsod
with. This instrument gave almost perfect satisfaction; and its accu-
racy will bo shown presently.

Tho tangent-galvanometer was also a very fine instrument, and was
constructed expressly for this series of experiments. The noodle was
1*1 inch long, of hardened stool; and its deflections were road on a
circle graduated to half degrees, and 5 inches in diameter. The aver-
age diameter of the ring was ICJ inches luuirly, and was wound with
several coils; so that the sensibility could hi‘ increased or diminished
at pleasure, and so give tho instrument a very wide range. Tlio value
of each eoil in producing defioelion was experimentally deterinmod to
within at hani of 1 per cent by a nuddiod which T shall soon publish.
Tho numb(‘rs to multiply tluj tang(‘nt of tlui deflcuttion by, in order to
reduce tho current to absolute measure, were as follows: —

Numbftrof col] a.

Mxiltlplior.

1 . .

. . . •05877

3 . .

. . . -01800

!) . .

. . . -OOfiOOr

27 . .

. . . -002018

48 . .

. . . -001143

By this instrument I had the means of measuring currents which
varied in strength several hmulrod times with the same accuracy for
a large as for a small current. For greater accuracy a correction was

Hbn-et a. Eowland

applied accoiding to tke formula of Blanchet and De la Prevostaye for
the length of the needle, the position of the poles "being estimated; this
correction in the deflections used was always less than -6 per cent. To
eliminate any error in the position of the zero-point, two readings were
always taken with the currents in opposite directions, each one being
estimated with considera'ble accuracy to 3^ of a degree.

The experiments were carried on in the assay laboratory of the
Institute, which was not being used at that time ; and precautions were
taken that the different parts of the apparatus , should not interfere
with each other. The disposition of the apparatus is represented in
Plate II.

The current from the battery A, of from two to six large Chester’s
electropoion ” cells No. 2, joined according to circumstances, passed
to the commutator B, thence to the tangent-galyanometer G, thence
to another commutator Z), thence around the magnet JE (in this case a
ring), and then back through the resistance-coils K to the battery. To
measure the magnetism excited in jP, a small coil of wire F was placed
around it,“ which connected with the gaWanometer H, so that, when
the magnetism was reyersed by the commutator D, the current induced
in the coil jP, due to twice cutting the lines of force of the ring,
produced a sudden swing of the needle of H, As the needle swung
very freely and would not of itself come to rest in ten or fifteen min-
utes, the little apparatus I was added: this consisted of a small horse-
shoe magnet, on one branch of which was a coil of wire; and by sliding
this back and forth, induced currents could be sent through the wire,
which, when properly timed, soon brought the needle to rest. This
arrangement was very efficient; and without it this form of galvano-
meter could hardly have been used. To compare the magnetism of
the ring with the known magnetism of the earth, and thus reduce it to
absolute measure, a ring 0 supported upon a horizontal surface was
included in the circuit; when this was suddenly turned over, it produced
an induced current, due to twice cutting the lines of magnetic force
which pass through the ring from the earth’s magnetism. The induced
current in the case of either coil, F or G, is proportional to the number
of the lines of force cut by the coils and to the number of wires in the
coil, which latter is self evirlent, but may be deduced from the law of
Gaugain.'^* It is eyident, then, that if c is the deflectiou from coil G,

If a bar was used, this coil was placed at its centre.

Faraday’s Experimental Besearches, vol. Hi, series 39.

^^Daguin’s TraiU J^ltyMque^ toI. iii, p. 691.

Magnetic Pekmbability oe Ikon, Steel and Nickel

and h that from helix F, the mimhcr of linos of force passing through
the magnet E, expressed in the unit wc have chosen, will ho

Q' = aM'(6-37 sin 74“ W

where is the number of coils in the rhi| 2 ; 0, ii the number in the
helix Fy 11 the radius of G, CJ- 27 the total magnetism of the earth, and
74°50' the dip. The quantity 2?i'(()*27 sin 74®50')7r22® is constant for
the coil, and had the value 14* 15. This is the number of square metres
of a unit field which, when cut once by a wire from the galvanometer,
would produce the same deflection as the coil when turned over.

The experiments being made by reversing tlie magnetism of the bars,
a rough experiment was made to see whether they had time to change
in half a single vibration of the needle; it was found that this varicul
from sensibly 0 to nearly 1 second, so that there was ample time. It
was also proved that the sudden impulse given to the needle by the
change of current produced the same deflection as when the change was
more gradual, which lias also been remarked by Faraday, though he
did not use such sudden induced currents. As a test of the method,
the horizontal force of the earth’s magnetism was determined by means
of a vertical coil; it was found to be 1-C34, while the true quantity is
1-641.

It is sometimes assumed that some of the action in a case like the
present is due to the direct induction of the helix arouTid the magnet on
the coil F, I think that this is not correct; for when the helix is of
fine wire closely surrounding the bar or ring, all the lines of force
which affect F must pass through the bar, and so no correction should
be made, TTowever, the eorroction is so small that it will hardly affect

the result. If it wore to he made, 9' (equation 5) should bo diminished

by 4;rilf; but, for the above reasons, it has not been subtracted. As a
test of the whole arrangement, I have obtained the number oE lines of
force in a very long solenoicb: the mean of two solenoids gave me

= 12-67

while from theory wc obtain, by equation (7) (/i = l),

Q = 12-67iK'(7rff»),

which is within the limits of error in measuring the diamoter of the
tubes, &c.

All the rings and bars with which I have experimented have had a
circular section. In selecting the iron, care must be used to obtain a

Henry A. Eowland

homogeneous bar; in the case of a ring I believe it is better to have it
welded than forged solid; it should then be well annealed, and after-
wards have the outside taken off all round to about of an inch deep in
a lathe. This is necessary, because the iron is burnt to a consider-
able depth by heating even for a moment to a red heat, and a §ort of
tail appears on the curve showing the permeability, as seen on plotting
Table III. To get the noimal curve of permeability, the ring must only
be used once; and the^i no more current must be allowed to pass through
the helix than that with which we are experimenting at the time. If
by accident a stronger current passes, permanent magnetism is given to
the ring, which entirely changes the first part of the curve, as seen on
comparing Table I with Table II. The areas of the bars and rings were
always obtained by measuring their length or diameter across, and then
calculating the area from the loss of weight in water. The following
is a list of a few of the rings and bars used, the dimensions being given
in metres and grammes. In the fourth column annealed means
heated to a red heat and cooled in open air, C annealed means placed
in a large crucible covered with sand, and placed in a furnace, where,
after being heated to redness, the fire was allowed to die out; natural
means that its temper was not altered from that it had when bought.

Results
Sriyen In
Table.

Qtiallty of
substance.

How made.

Temper.

Spec.

gray.

Weight

Mean

dlam.

Area.

St*itc.

“Burden
best” iron.

Welded and
turned.

Annealed.

US- Cl

•0077

•oooo

916

Normal.

II.

iC ((

((

^7-08

148- Cl

•0(577

016

Magnetic.

HI.

(( ((

1 (

C an-
nealed.

j. 7-158

148-01

•0077

013

Burnt,

IT. j

Bessemer

steel.

Turned from
large bar.

Natural.

7-84

88-84

•0420

871

Normal.

{

Norway

iron

Welded and
turned.

C an-
nealed.

|7-88

80-78

-065C

7000

Magnetic.

vr.{

Cast
nickel. «

Turned from
button.

—

8-88

4-80C

•0300

08(50 Normal.

VII. 1

Stubs’

steel.

Hard-drawn

wire.

Natural.

7-78

....

OOCoj Normal.

• The first three Tables are from the same ring.

Besides these I have used very many other Imrs and rings; hwt most
of them were made before I had discovered tin* ofToct of Imrning upon

Almost chemically pure before melting.

Maon’btio Permeability ob Iron, Steel and Nickel 45

tlie iron, and hence did not give a normal curve for high magnotizhig-
powers. Ho-wever, I have collected in Tabic VIII some of the results
of these experiments; but I have many more ■which arc not worked
up yet.

In the following Tables Q = has been nioasured jus previously

described. It is evident that if, instead of reversing the current, we
simply break it, we shall obtain a deflection due to the temporary mag-
netism alone. In this manner the temporary magnetiBiii has been
measured; and on subtracting this from (?, we can obtain the permanent
magnetism.

The following abbreviations are made use of in the Tables, the other
quantities being tlic same as previously dcseribod.

0,T.G. Number of coils of tangent-galvanometer used.

D.T.&, Deflection of tangent-galvanometer.

D.C. Deflection from coil 0.

D.F. Deflection from helix F on reversing the cnirrent.

Q. Magnetic field in interior of bar (total).

D,B. Deflection from F on breaking current,
r. Magnetic field of bar due to t(nni)orary inagnc^tisni.

P. Magnetic field of bar due to permanent magnotisTn.

11 , Number of coils in helix P.

Q = T + P.

Each observation given is almost always the m(3aii of several . D.T.O,
is the mean of four readings, two before and two after the ohsovvations
on the magnetism; J).0. is tlie mean of from four to ten readings; D.F,
mean of three; D.B, moan of two, except in Tables I, where the deflec-
tion was road only on<jo. In all these Tal)les the column containing
the temporary magnetism T can only bo accepted as approximate, the
experiments having been made more* to deterinine Q than T.

The value of n was generally varied l)y coiling a wire more or less
around the ring, l)ut leaving its length the same.

The change in the value of D.O. is diu* to the change in the resist-
ance of the galvanometer from (diango of temperature, copper wire
increasing in resistance about 1 per cent for every 0. rise. In
Table I the temperature first Increased slowly, and thou, after remain-
ing stationary for a while, fell very fast.

HBisrET A. Eowland

16 TABLE 1.

Burden Bbbt” Ibost, Normal.

lE*

O.T.G.

D.T.G.

D.O.

D.F.

D.P.

2n. *

D.B.

Oalou-

lated.

M-JJ.

M.*

4-6

-1466

28-4

6-5

‘1088

•08

716

4910

6846

628

187*

1284-

-6601

54-6

-910

•69

10920

10886

868-7

8894

2111-

8888-

7748*

-6816

87-9

1-466

•80

9667

1418(]

14074

1129

4887-

Wti f ■

8786-

28-6

1-011

^'•8

74-2

8-71

1-84

1986

8882

15718-

nvIvE

8766-

fli-i

1-119

4-41

1*48

29280

Ki'iMll

9811

19419-

pvtixiB

Mifl-

1.166

4-68

1-68

26660

2124

17870-

41-12

1-628

29*8

7-46

2-0

49690

80670

2488

86280-

22870-

28-85

1-766

28-1

82-8

2-6

64820

16710

88110-

21670-

96l7‘

29-6

1-861

84-6

8-66

2-65

67820

■ifTr/jl,

2472

17710

EdfliJI

21650-

8R19-

88-4

2-162

ai-1

89-fi

9-05

2-85

66610

80770

■tMil

2448

19060

47460-

21950-

87-46

2-612

44-7111-18

8-06

74780

29750

29980

2867

rTi’i I'B

21680-

7986'

44-46

8*228

68-618-88

8-85

89480

27760

27890

2208

1 1 iT'B

7fl7i*

62-1

4-225

60-8

16-08

4-85

28860

24780

1899

■*it ivB

84-65

6-744

78-118-28

7-10

18210

18410

1448

S JViVi

11180’

6519-

89-8

8-186

77-8

19-82

7-90

15940

16180

1269

1-tCvri

76660-

9428-

6408-

44-8

9-642

40-6

9-1

KviVr

18920

1187

75200-

4666-

66-1

14-04

48-621-75

9-8

mmsM

8»-l

65610

79890-

2816 -

’a

42-95

27-18

1 Yf’f '■

6860

461-8

81160-

2985-

61-8

■ liwyflV

4528

858.8

84180

78620-

2146-

60-16

61-18

28-4

••

18-2

8248

8810

268.0

87120

78080-

1541-

TABLE II.

“Bubdbe Bust’’ Iron, Magnetic.

V -

•1456

426

2920

282

2-930

28240

2247

•6699

8346

5987

476

4-210

100900

28960

1906

•0962

8189

652

6-769

122800

18140

1444

1795

7.278

124800

17090

1360

1-191

29280

24580

1956

7-626

16670

1826

1-687

46160

2889

11-10

12570

1000

bBI

2408

18-61

144700

10680

846

1- 988

2- 877

59680

71660

■

2456

2890

22-10

154000

6965

564

i« TABLE III.

“Burden Best” Iron, Burnt.

fi.

•148

1001

7089

660

1020

8.810

116900

80780

2446

,658

9896

10980

1351

5115

4-288

120300

28060

2288

4280-

•682

16650

24240

1929

6885

! 4-722

128900

26240

2088

80880

9715-

•962

37880

38780

8086

9451

1 6.505

188100

20270

1613

27876-

1-070

42920

40180

8194

10800

1 9-826

141200

16140

1200

80810

82620-

1-158

48880

42840

8869

10680

11-00

144400

18130

1046

88800-

1-817

59490

46180

8596

11650

18-44

147500

10970

878

4407047840-

10S4SO-

1-340

59580

44450

8588

18700

28-41

155600

6643

529

61080

46880-

104470-

2-127

90180

42400

8874

18470

32-78

159400

4870

887

71710-

2-601

98560

89400

8186

19920

82-66

158400

4864

887

78640-

2-804

104000

80810

2890

24600

61-08

165800

8260

269

66100

79400-

109700-

8-161

108200

84880

2732

24610

88590-

i^EGoluinns 1, 16, 16 were added to the original paper by Professor Bowland,
after its publication.]

i«[The last two columns of Tables III, IV, V, VII were added by Professor Row-
land after the paper was published.]

TABLE VI.

Oast Nxokbl, Noumal.

M-

1-488

852

47-4

18-48

27100

2018

160-6

nseo

2-904

2877

819

65-1

16-68

81050

1878

140-5

18580

8-527

8685

1070

85-1

21-02

84950

1668

182-8

10480

5-565

10080

1816

144-4

83-17

41980

1805

108-8

22800

6-788

18680

2017

160-5

5120

88-92

42650

1267

100-0

28860

7-401

15270

2088

164-2

5014

60-91

50860

H55

66-4

29540

9-278

19600

2114

168-2

7644

83-36

58650

651

51.8

88460

11.78

24720

2098

167-0

9902

105-2

55280

525

41-8

85120

TABLE VII.

Studs’ Stbbl Wxrb, Koumai..

/*.

M-

•1678

159

958

75-9

18-65

54800

S97H

816-6

20900

88400-

•6287

678

1087

86-5

598

19-85

77770

4020

819-9

29480

80-

48200-

1.084

1197

1104

87-9

1101

27-43

100800

3670

292-6

88590

96-

62210-

2-048

2448

1199

95-4

2257

88-89

111800

8885

265-4

45110

191-

66190-

2-714

8446

1270

101-0

8095

85-68

115000

8228

256-9

45050

851-

69050-

4-221

0278

1487

118-4

5145

88-64

119400

8092

246-0

48060

1188-

71840-

10-26

88700

8286

261-5

16170

17530-

4:8

Henbt a. Howland

The best method of studying these Tables is to plot them: one
method of doing this is to take the value of the magnetizing-force as
the abscissa, and that of the permeability as the ordinate; this is the
method used by Dr. Stoletow; but, besides making the complete curve
infinitely long, it forms a very irregular curve, and it is impossible to
get the maximum of magnetism from it. Another method is to employ
the same abscissas, but to use the magnetism ,of the bar as ordinates;
this gives a regular curve, but has the other two disadvantages of the
first method; however, it is often employed, and gives a pretty good
idea of the action. In Plate II, I have given a plot of Table V with
the addition of the residual or permanent magnetism, which shows the
general features of these curves as drawn from any of the Tables. It
is observed that the total magnetism of the iron at first increases very
fast as the magnetizing-force increases, but afterwards more and more
slowly until near the maximum of magnetism, where the curve is
parallel to the axis of Q. The concavity of the curve at its commence-
ment, which indicates a rapid increase of permeability, has been noticed
by several physicists, and was remarked by myself in my experiments of
January, 1871; it has now been brought most forcibly before the public
by Dr. Stoletow, whose paper refers principally to this point." M.
Muller has given an equation of the form

/= tan

^ 000053 *

to represent this curve; but it fails to give any concavity to the first
part of the curve. A formula of the same form has been used by M.
Gazin;” but his experiments carry little weight with them, on account
of the small variation of the current which he used, this being only
about five times, while I have used a variation in many cases of more
than three hundred times.

Veber has obtained, from the theory that the particles of the iron
are always magnetic and merely turn round when the magnetizing-
force is applied, an equation which would make the first part of the
curve coincide with the dotted line in Plate II;” and Maxwell, hy addi-
tion to the -theory, has obtained an equation which replaces the first

On the Magnetizing Function of Soft Iron, especially 'with the -weaker decom-
posing po-wers. By Dr. A. Stoletow, of the University of Moscow. Translated in
the Phil. Mag., Jannary, 1878. See particularly p. 43.

^8 AnnaUi de Chimie et de PhyHqw, February 1878, p. 183.

19 This is according to Maxwell’s integration of Weber’s eq.uatioii, Weber having
made some mistake in the integration.

Hbntit a. EotoiAND

in wMah. A, E, D, and a are constants depending upon the kind and
quality of the metal used. A is the maxunttm value of A, and gives
the height of the curve H B, Plate HI; a establishes the inclination of
the diameter; JT is the line AOj and D depends upon the line A 0.
The following equation, adapted to degrees suid fractions of a degree,
is the equation from which the values of i were found, as given in
Table I:

1 = 31-100 sin 1^:6 ^ J.

The large curve in Plate HI vas also drawn from this, and the dots
added to show the coincideuce with observation; it is seen that this is
almost perfect. As 1 enters both sides of the equation, the calculation
can only be made by successive approximations. We might indeed solve
with reference to Qj but in this case some values of 1 as obtained from
ejcperiment may be accidentally greater than A, and so give an imagi-
nary value to Q.

By plotting any Table in this way and measuring the distance 0 0,
we have the maximum of magnetism.

I have given in the same Plate the curve drawn from the observations
on the nickel ring with Q on the same scale, but A on a scale four times
as large as the other. The curve of nickel satisfies the equation

quite well, hut not so exactly as in the case of iron. This ring, when
closely examined, was found to be shghtly porous, which must have
changed the curve slightly, and perhaps made it depart from the
equation.

In Table VIII, I have collected some of the values of the constants
in the formula when it is applied to the difEerent rings and bars, and
have also given some columns showing the maximum of magnetism.
When any blank occurs, it is caused by the fact that for some reason
or other the observations were not sufSlcient to determine it. The
values of a, JET, D, and the value of when 0 = 0, can in most cases
only he considered approximate; for as they all vary so much, I did not
think it necessary to calculate them exactly. For comparison, I have
plotted Dr. Stoletow’s curve and deduced the results given in the Table,
of course reducing them to the same units as mine.

It will be observed that the columns headed ''maximxtm of mag-
netism" contain, besides the maximum magnetic field, two columns

TABLE Vni

Machtetio Pebmeabilety OB laoN, Steel and ITiOBaiL 61

mTMb satisfies all except the last few observations, wblcb constltntes the “ tail *» before referred to.

Henet a. Rowland

giving the tension of the lines of force per square centimetre and square
inch of section of the lines. These have been deduced from the formula

given by Maxwell for the tension per square metre, which is ^

OTT

absolute units of force.

This becomes

0 * 1
^WOOOOO P®^ oentim , |

(13)

from which the quantities in the Table were calculated.

It is seen that the maximum of magnetism of ordinary bar iron is
about 176,000 times the unit field, or 177 lbs. on the square inch, and
for nickel 03,000 times, or 23*9 lbs. on the square inch. For pure iron,
however, I think it may reach 180,000, or go even above that. It is
seen that one of the Norway rings gave a very high result; this is
explained by the following considerations. Alt the iron rings were
welded except this one, which was forged solid from a bar 2 inches
wide and then turned. Even the purest bar iron is somewhat fibrous ;
and between the fibres we often find streaks of scale lying lengthwise
in the bar and so diminishing the section somewhat if the ring be
welded from the bar; when, however, it is forged solid, these streaks
are thoroughly disintegrated; and hence we find a higher maximum
of magnetism for a ring of this kind, and one approaching to that of
pure iron. But a ring made in this way has to be exposed to so much
heating and pounding that the iron is rendered unhomogen eous, and a
tail appears to the curve like that in Table III. It is evident that this
tail must always show itself whenever the section of the ring is not
homogeneous tlirougbiout.

Hence wo may conclude that the greatest weight which can he sus-
tained by an electromagnet with an infinite current is, for good but not
pure iron, 354 lbs. per square inch of section, and for nickel 46 lbs.

Joule®* has made many experiments on the maximum sustaining-
power of magnets, and has collected the following Table, which T give
complete, exce])t that I have replaced the result with his large magnet
by one obtained later.

It is seen that those are all below my estimate, as they should bo.

23 Treatise on Electricity and Maj^netism, vol. ii, p. 350.
24 Phil, Mag., 1851.

Magnetic Pekmeability of Iron, Steel and Nickel 53

l''or comparison, I have added a column giving the values of Q which
would give the sustaining-power observed; some of these are as high
as any I have actually obtained, thus giving an experimental proof that
my estimate of 354 lbs. cannot be far from correct, and illustrating
the beauty of the absolute system of electrical measurement by which,
from the simple deflection of a galvanometer-needle, we are able to
predict how much an electromagnet will sustain without actually trying
the experiment.

TABLE IX.

Magnet belonging to

Ijeast aroii of
section, squaro
inch.

Weight

sustained.

Weight sus-
tained +
least area.

10.

•190

2775

277

154700

^ . (2

250

147000

•0480

275

154100

•0012

■202

162

118800

Mr. Nesbit

4-0

1428

817

106500

Prof. Henry

:M)4

750

190

128200

Mr. Sturgeon .......

• 190

255

148500

Ill looking over the columns of Table VIII, wliicdi contain the values
of the constants in the fonniila, we sec how futile it is to attempt to
give any fixed value to tlie penneabiliiy oL* iron or nicjkel; and wo also
see of how little value cxperiiiKMits on any one kind oL* iron are. Iron
differs as much in magnetic permealiility as copiier docs in electric
conductivity.

It is seen that in the thr(‘e cases when iron bars have been used, the
value of a is negative; wo might consider fhis to he ti gcmoral law, if I
(lid not possess a ring whi(th also gives this negative. All those hats
hud a length of at had 120 times their diameter.

The mathematical ih(‘ory of magnetism has always heem (‘onsidcred
one of the most difficult of subjects, even whem, as heretofore, fx is
considered to ho a constant; hut mmu when it must Ixi taken as a func-
tion of the magnotism, the (Iini(*nlly is increased many fold. There arc
certain cases, however, wh(u*(^ fhe magnetism of the body is uniform,
which will not bo ufTected,

Troy^ 2, 1 87a.

PLATE II.

( 64 )

PLATE III.

( 65 )

[Curves P and T were added by Professor Rowland to the original diagram.]

ON THE MAGNETIC PBRMEABILirY AND MAXIMUM OP
MAGNETISM OP NICE:EL AND COBALT

[PMoiopAicaZ Magazine [4], XL VJII, 821-340, 1874]

Some time ago a paper of mine on the magnetic permeability of iron,
steel, and nickel vas published in the Philosophical Magurinc (August,
1873); and the present paper is to be considered as a continuation of
that one. But before proceeding to the experimental results, I should
like to make a few remarks on the theory of the subject. The mathe-
matical theory of magnetism and electricity is at present developed in
two radically diSerent manners, although the results of both methods of
treatment are in entire agreement with experiment as far as we can
at present see. The first is the German method; and the second is
Paraday’s, or the English method. When two magnets are placed near
each other, we observe that there is a mutual force of attraction or
repulsion between them. Now, according to the German philosophers,
this action takes place at a distance without the aid of any intervening
medium: they know that the action takes place, and they know the
laws of that action; but there they rest content, and seek not to find
how the force traverses the space between the bodies. The ’B’.ngHa'h
philosophers, however, led by Newton, and preeminently by Faraday,
have seen the absurdity of the proposition that two bodies can act upon
each other across a perfectly vacant space, and have attempted to ex-
plain the action by some medium through which the force can be trans-
mitted along what Faraday has called “ lines of force.”

These differences have given rise to two different ways of looking
upon magnetic induction. Thus if we place an electromagnet neat a
compass-needle, the Germans would say that the action was due in part
to two causes ^the attraction of the coil, and the magnetism induced in
the iron by the coil. Those who hold Faraday’s theory, on the other
hand, would consider the substance in the helix as merely “ conduct-
ing ” the lines of force, so that no action would be exerted directly on
the compass-needle by the coil, but the latter would only affect it in
virtue of the lines of force passing along its interior, and so there could
be no attraction in a perfectly vacant space.

Magnetic Permeability of Nickel and Cobalt

According to the first theory, the magnetization of the iron is repre-
sented by the excess of the action of the electromagnet over that of the
coil alone ; while by the second, when the coil is very close around the
iron, the whole action is due to the magnetization of the iron. The
natural unit of magnetism to be used in the first theory is that quantity
which will repel an equal quantity at a unites distance with a unit of
force; on the second it is the number of lines of force which pass
through a unit of surface when that surface is placed in a unit field
perpendicular to the lines of force. The first unit is 4:7c times the
second. Now when a magnetic force of intensity acts upon a mag-
netic substance, we shall have = in which Sis the mag-

netization of the substance according to Paraday^s theory, and is what
I formerly called the magnetic field, but which I shall hereafter call,
after Professor Maxwell, the magnetic induction. Qf is the intensity
of magnetization according to the German theory, expressed in terms
of the magnetic moment of the unit of volume. Now, when the sub-
stance is in the shape of an infinitely long rod placed in a magnetic field

parallel to the lines of force, the ratio ^ is called the magnetic

permeability of the substance, and the ratio ^ — k is Neumann^s co-

•y

efficient of magnetization by induction. Now experiment shows that
for large values of .sj the values of both /i and k decrease, so that
we may expect either or both and 3 to attain a maximum value.

In my former paper I assinnod that 93 as well as ^ attain a maxi-
mum; but on further considering the subject I see that we have no data
for determining which it is at present. If it wero y)opsiblo for 93 to
attain a maximum value so that [i should a])])roach to 0, k would be
negative, and the substanc(» would then hocoino diamagnetic for very
high magnetizing forces." This is not contrary to observation ; for at
present wo lack the nuums of producing a sufficiontly intense magnetic
field to test this oxporiniontally, at least in the (taso of iron. To pro-
duce this effect at ordinary toinporaturos, we must liavo a magnetic field
greater* than the followung— for iron 175,000, for nickel 011,500, and for

^ r shall horcaftor in all my papers use tlio notation as ^ifivon In Professor Maxwell’s
* Treatise on Electricity and Ma^notiflin ; ’ lor comparison with my former paper 1
give the following :

58 in this paper = Q In former one,

£i “ = 4frM “

3 “ =®-M ..

’See Maxwell’s ‘Treatise on Electricity and Magnetism,’ art. 844. — J. 0, M.

Hbn’rt a. Eowland

cobalt about 100,000 (?). These q^uantities are entirely beyond our
reach at present, at least mth any arrangement of solenoids. Thus,
if we had a helix 6 inches in diameter and 3 feet long with an aperture
of 1 inch diameter in the centre, a rough calculation shows that, with
a battery of 350 large Bunsen cells, the magnetic field in the interior
would only be 15,000 or 20,000 when the coils were arranged for the
best effect. We might obtain a field of greater intensity by means of
electromagnets, and one which might be suflEicient for nickel; but we
cannot be certain of its amount, as I know of no measurement of the
field produced in this way. But our principal hope lies in heiatiag some
body and then subjecting it to a very intense magnetizing-force; for I
have recently found, and will show presently, that the maximum of
magnetization of nickel and iron decreases as the temperature riseSy at
least for the two temperatures 0° 0. and 220° C. I am aware that iron
and nickel have been proved to retain their magnetic properties at high
temperatures, but whether they were in a field of sufficient intensity at
the time cannot be determined. The experiment is at least worth try-
ing by some one who has a magnet of great power, and who will take
the trouble to measure the magnetic field of the magnet at the point
where the heated nickel is placed. This could best be done by a small
coil of wire, as used by Yerdet.

But even if it should be proved that S5 does not attain a maximum,
but only 3; it could still be explained by Faraday^s theory; for we
should simply have to suppose that the magnetic induction S was
composed of two parts — ^the first part, 4;r3[, being due to the magnetic
atoms alone, and the second, to those lines of force which traversed
the aether between the atoms. To determine whether either of these
quantities has a maximum value can probably never be done by experi-
ment; we may be able to approach the point very nearly, but ca^ never
arrive at it, seeing that we should need an infinite magnetizing-force to
do so. Hence its existence and magnitude must always be inferred
from the experiments by some such process as was used in my first
paper, where the curve of permeability was continued beyond the point
to which the experiments were carried. Neither does experunent up
to the present time furnish any clue as to whether it is 35 or which
attains a maximum.

As the matter is in this undecided state, I shall hereafter in most
cases calculate both and k as well as S3 and fi, as I am willing to admit
that 3 have a physical significance as well as 33, even on Faraday’s
theory.

Magnetic PesiieabiiiItt oe Nickel and Cobalt

There ia a difficulty in obtaining a good aeries of experiments on
nickel and cobalt which does not exist in the case of iron. It is prin-
cipally owing to the great change in magnetic permeability o£ these
substances by heat, and also to their small permeability. To obtain
sufficient magnetizing-force to trace out the curve of permeability to a
reasonable distance, we require at least two layers of wire on the rings,
and have to send througli that wire a very strong current. In this way
great heat is developed; and on account of there being two layers of
wire it cannot escape ; and the ring being thus heated, its permeability
is changed. So much is this the case, that when the rings are in the
air, and the strongest current circulating, the silk is soon burned off the
wire; and to obviate this I have in these experiments always immersed
the rings in some non-conducting liquid, such as alcohol for low tem-
peratures and melted paraffin for high temperatures, the rings being
suspended midway in the liquid to allow free circulation. But I have
now reason to suspect the efficacy of this arrangement, especially in the
case of the paraffin. The experiments described in this paper were
made at such odd times ns I. could command, and the first ones were not
thoroughly discussed until the series was almost completed; hence 1
have not been so careful to guard against this error as I shall be in the
future. This can be done in the following manner — ^namely, by letting
the current pass through the ring for only a shirt time. But there is a
difficulty in this method, because if the current is stopped the battery
will recruit, and the moment it is joined to the ring a largo and rapidly
decreasing current will jiass which it is impossible to measure accu-
rately. I have, however, devised the following method, which I will
apply in future experiments. It is to introduce into the circuit between
the tangent-galvanometer and the ring a curront-changor, hy which the
current can he switched off from the ring into another wire of the same
resistance, so that the current from the battery shall always be con-
stant. Just before making an obsorvation the current is turned back
into the ring, a reading is taken of the tangont-galvanoineter by an
assistant, and immediately afterward the current is reversed and the
reading taken for the induced current; the tangent-galvanometer is
then again read with the needle on the other side of the zero-point.
The pressure of outside duties at present precludes me from putting this
in practice. But the results which I have obtained, though probably
influenced in the higher inagnetizing-forces by this boating, are still
so novel that they must possess value notwithstanding this defect; for
they contain the only experiments yet made on the permeability of

Heitet a. Rowland

cobalt at ordinary temperatures, and of iron, nickd, and cobalt at high
temperatnres-

The rings of nickel and cobalt which I have used in the experiments
of this paper were all turned from buttons of metal obtained by fnsing
under glass in a French crucible, it having been found that a Hessian
crucible was very much attacked by the metal. The crucibles were in
the fire three or four hours, and when taken out were very soft from
the intense heat. As soon as taken out, the outside of the crucible was
wet with water, so as to cool the metal rapidly and prevent crystalliza-
tion; but even then the cooling inside went on very slowly. As the
physical and chemical properties of these metals exercise great infiuence
on their magnetic properties, I will give them briefly. A piece of nickel
before melting was dissolved in HCl; it gave no precipitate vrith ffS,
and there were no indications of either iron or cobalt. A solution of
the cobalt gave no precipitate with H^S, but contained small traces of
iron and nickel. After melting the metals no tests have been made up
to the present time; but it is to be expected that the metals absorbed
some impurities from the crucibles. They probably did not contain
any carbon. One button of each metal was obtained, from each of
which two rings were turned. The cobalt was quite hard, but turned
well in the lathe, long shavings of metal coming ofE and leaving the
metal beautifully polished. The metal was slightly malleable, but fin-
ally broke vrith a fine granular fracture. The rings when made were
slightly sonorous when struck; and the color was of a brilliant white
slightly inclined to steel-color, but a little more red than steel. The
nickel was about as hard as wrought iron, and was tough and difficult
to turn in the lathe, a constant application of oil being necessary, and
the tamed surface was left very rough; the metal was quite malleable,
but would become hard, and finally fly apart when pounded down thin if
not annealed. When, the rings were struck, they gave a dead sound as
if made of copper. In both cases the specific gravity was considerably
higher than that generally given for cast metal; but it may be that the
metal to which they refer contained carbon, in which case it would he
more easily melted. There is great liability to error in taking the
specific gravity of these metals, because they contract so much on cool-
ing, and unless this is carried on rapidly crystals may form, between
which, as the metal contracts, vacant spaces may he left. As the
specific gravity of my rings approaches to that of the pure metals pre-
cipitated by hydrogen, I consider it evidence of their purity. The
dimensions of the rings and their other constants are as follows: —

Magnetic Peemeabilitt of I^ickel and Cobalt

Rlngr.

Weight in
vacno, in
grammoH.

Loss in water
at 4° 0.,lu
grammes.

Speclflo

gravity.

Moan dia-
meter, In
centimetres.

Nickel, No. I

21-838

3-4560

8-886

8-28

Nickel, No. II

....

8-887

.*. . .

Cobalt, No. I

10-011

1 • 1435

8-7663

2-48

Cobalt, No. II

4-081

■!i84C

8-7550

1-81

Mean olrcum-j

Number of

Ooils per

Area of bog-

Jllng.

ferenoe, in
centimetres.

coils of wire
on ring.

metre of olr-
oumferenco.

tlon, in square
oontlmecres.

Nickel, No. I

10-804

318

3086

-3384

Nickel, No. II

. • • ■

....

Cobalt, No. I

7-791

343

8119

-146T

Cobalt, No. II

5-686

168

3779

-09403

Up to the present time only the rings whose dimensions are given
have been -used.

The following Tables from the nickel ring No. I leave little to be
desired in point of regularity, and confirm the fact proved in my first
paper, that the laws deduced for iron hold also fox nickel, and also
confirm the value given in my other paper for the maximum value of
magnetization of nickel. But the most important thing that they show
is the effect of heat upon the magnetization of nickel; and Table HE
contains the first numerical data yet ol)taincd on the effect of heat on
the magnetic properties of any substance.

As all the rings were wound with two layers of wire, a slight correc-
tion was made in the value of 39 for the lines of inductive force which
passed through the air and not through the metal. In all the experi-
ments of this paper greater care was used to obtain T than in the first
paper. Each value of 33, and T is the mean of four readings. In
all the Tables I liave left the order of tlic observations the same as that
in which they wiu’O nifidis and have also put down the date, as I now
have reason to sus])ecit that the leaving of a ring in the magnetized state
in which it is after an oxporimont will in time affect its properties to a
small (‘xtent. Let me here remark that, the time nocopsary to simply
make the observations is only a very small fraction of that required to
prepare for them and to afterwards discuss them. And this, with, the
small amount of time at my disposal, will account for the late day at
which I publish my results.

The following is the notation used, the measurements being made on
that absolute system in which the metre, gramme, and second are the
fundamental units.

Henry A. Rowland

^ is the magnetizing-force acting on the metal.

S is the magnetic induction within the metal (see Maxwell’s ^ Trea-
tise on Electricity and Magnetism/ arts. 400^ 592, and 604).

/i is the magnetic permeability of the metal =:^=4:rK+l.

T is the portion of SB which disappears when the current is broken.
P is the portion of SB which remains when the current is broken.

3 is the intensity of magnetization

K is Ifeumann’s coefficient of induced magnetization =^.

TABLE I.

Cist Niokbl, Normal, at C.
Experiments made November 29, 1873.

■'(ite.

served.

Cafou-

lated.

Error.

3 .

Ob-

served.

Calcu-

lated.

Error.

12-84

676

62*6

4a -4

—6-2

52-7

4-10

8-65

— -46

26-85

2169

80*8

80-6

— -2

1268

170-6

6-86

6-27

— 08

45-14

7451

165-1

166-8

1-7

2894

4.557

.589-8

18-06

18-08

•02

66-12

11140

198-6

199-1

•6

8788

7852

882-0

15-72

15-70

— 02

70-78

15410

217-8

217-6

— -8

6018

10892

1221

17-25

17*21

— 04

77-62

17100

220-6

•0

6454

11646

1356

17-47

90-76

20180

222-8

222-0

— -3

6488

18697

1699

17-61

17-60

—01

115-4

26170

218-2

214-8

—8 -9

8318

16867

1994

17-28

16-98

— 80

189-4

28640

904-7

204-8

— .4

lOlOO

18440

2260

16-21

16-18

—.08

172-9

82460

187-8

186-6

-1-2

12580

19980

2569

14-86

14-98

•07

195-8

84680

177-8

179-1

1-8

18820

21810

2740

14-08

14-12

•09

229-5

87840

162-8

166-5

2-7

16720

21620

2958

12-87

18-02

■16

275-9

40860

148-1

146-8

-1-8

17960

22900

8280

11-71

11-46

— 26

415-2

46470

111-9

112-8

•9

22560

28910

8665

8-82

8-77

— 05

727-0

52690

72-5

72-8

•3

28020

24670

4186

6-69

5-64

— 06

1042

55680

58-4

62-8

— -6

80680

25000

4844

4-17

—

68420

....

—

4940

—

/I =222 sin

/93-f 63^-HISOO

/c=17 6 Bin

/3 + 50«: + 100\
[ /

TABLE II.

Cast Niokbl, Magubtio, at 12° C.
Experiments made December 6, 1873.

-ft.

».

3 .

28-25

1245

58-65

97-2

4-18

47-69

7786

168-8

8095

4691

616-8

12-91

67-78

11460

198-3

8740

7730

907-3

i.a-70

78-43

16040

2]8-5

6082

11008

1270-6

17-30

88-28

19790.

224-8

6554

18286

1568

17-77

107-8

28580

219-2

7620

1.5910

1864

17-86

168-8

80X60

196-1

10940

19220

2888

16-52

206-8

8.5880

174-0

14080

31860

2889

18-76

296-4

41810

139-4

18890

22920

8264

11-01

421-8

46530

110-8

22520

34000

8668

8-70

Magnetic Permeabilitt oe Nickel and Cobalt

TABLE III.

Cast Niokbl, Magnetic, at 220® C.

Experljnents made December 6, 1878.

$8.

lA..

22-60

4502

199-2

2671

1881

856-4

16-77

16 -os

14000

810-8

5470

8680

nil

24-65

52-96

16660

814-6

6860

10810

1822

24-96

67-42

20800

301-1

77S3

12678

1602

28-88

80-69

22540

279-8

8914

18626

1787

22-16

106-4

26420

248-8

11140

16280

2094

10-68

160-8

30740

203-8

14040

16700

2484

16-14

191-0

88580

176-6

16940

17690

2668

18-89

294-8

88800

129-9

20240

18060

8024

10-26

558-6

42680

77-0

24860

18270

8848

6-05

789-8

48000

B5-6

26060

17840

8481

4-846

SxperimentB made December 10,

1878.

18-00

1687

118-3

109-2

9-88

32-87

4262

190-5

887-4

16-08

25-16

5387

212-2

» • • •

422-7

16-81

88-19

9486

286-8

4065

5481

763-8

22-15

48-28

18570

818-6

5867

8218

1070

24-88

la Table I are given the Tesnlts for nickel at about 16® 0., together
vith the values of /* and « calculated from the f ormulse given boloiv the
Table. We see that the coincidence is almost perfect in both cases,
which thus shows that the formula which we have hitherto used for A
and A can also be applied to at least within the limit of experiments
hitherto made, although it must at last depart from one or the other
of the curves. The greatest relative error is seen to be in the first
line, where ^ is smaE: this does not indicate any departure from the
curve, but is only due to the too small deflections of the galvanometer j
and the error indicates that of only a small fraction of a division at the
galvanometer.

In the calculation of and k a method was used which may be of
use to others in like circumstances, who have to calculate a large num-
ber of values of one variable from a function which cannot be solved
with reference to that variable, but can be solved with reference to the
other. Thus we have

/. = /Sein(^±^i±5) (1)

which can be solved with reference to ® but not to //; for we have

8 = JJ sin-*^^^— V — (*)

HeNBT a. EOWIiAKD

Suppose we have values of S, and wish to find the corresponding values
of We first calculate a few values of 33 from (3) so that we can plot
the curve connecting 33 and fji. We then from the plot select a value
of which we shall call fi', as near the proper value as possible, and
calculate the corresponding value of S3, which we shall call 33'. Our
problem then is, knowing 33' and /t', to find the value of /i corresponding
to 33 when this is nearly equal to 33'. Let 33' receive a small increment
.^33', so that S3 = S3' + JS3' ; then we have, from Taylor’s theorem, since
;/ = p (S3' + iS3') and pi = y>(S3')j

^ + % C^®') + \ C^S')’ + &c.

Eememtering that the constants in (1) refer to degrees of arc and
not to the absolute value of the arc, yre have

which is in the most convenient form for calculation by means of
Barlow^s Tables of squares, &c., and is very easy to apply, being far
easier than the method of successive approximation.

On comparing the magnetic curve Table II with the normal curve
Table I, we see that the magnetic curve of nickel bears the same rela-
tion to the normal curve as we have already found for iron; that is,
the magnetic curve falls below the normal curve for all points before
the vertex, but afterwards the two coincide.

Hence we see that at ordinary temperatures the magnetic properties
of nickel are a complete reproduction of those of iron on a smaller scale.
But when we come to study the effect of temperature we shall find a
remarkable difference, and shall find nickel to be much more susceptible
than iron to the influence of heat.

In Table III we have experiments on the permeability of nickel at
a high temperature, the ring being maintained at 320° 0. by being
placed in a bath of melted paraffin : in this bath the silk covering of
the wire remained quite perfect, but after many hours became some-
what weak. After completing the experiments on this and the cobalt
rings, on unwinding some of them I found the outside layer quite per-
fect; hut, especially iu the smallest ring, the silk on the inside layer
was much weaker, although the insulation was still perfect when the
wire was in place. I can only account for this by the electric current
generating heat in the wire, which was unable to pass outward because

Magnbtio Pbembabiiity of NiokbIi and Cobalt

of the outside layer and also of the pieces of paper -which were used to
separate the layers of -wire; hence the ring at high magnetizing-poweis
must have been at a somewhat higher temperature than.the bath, to an
amoimt which it is impossible to estimate. It is probable that it was
not very great, however; for at this high temperature continued for
hours it requires but little increase of heat to finally destroy the silk.
We can, however, tell the direction of the error.

We see, on comparing Tables I and II with Table III, the great
effect of heat on the magnetic properties of nickel. We see that for
low magnetization the permeability is greatly increased, which is just
opposite to what we might expect; but on plotting the curve we also
notice the equally remarkable fact, that the maximum of magnetization

is decreased from sg=:63,400 or3f=*4940 to !B=49,000 or 3=8800.
This curious result is shown in the annexed figure, where we see that
for low magnetizing-forces // is increased to about three or four times
its value at 16® 0., and the maximum value of fi is ineroasod from %%%
to 816. When SB has a value of 32,000, ji is not affected by this change
of temperature, seeing that the two curves coincide; but above that
point fi is less at 220° 0. than at 15° 0. In other words, if moM is
heated from 16° 0 . to 220° 0., the magnetization of nicTeel will increase if
the magnetizmg-foroe is small, hit wiU decrease if it is large. It is impos-
sible to say at present whether increase of temperature above 220° will
always produce effects in the same direction as below it or not.

These remarkable effects of heat, it seems to me, -will, when followed
out, lead to -the discovery of most important connections between heat
and magnetism, and -will finally res-ult in giving us much more light
upon the nature of heat and magnetism, and that equally important
s

Hbitet a. Eowland

question of what is a molecule. To accomplish this we must obtain a
series of curves for the same ring between as wide limits of temperature
as possible. We must then plot our results in a suitable manner; and
from the curves thus formed we can find what would probably happen
if the temperature were lowered to the absolute zero, or were increased
to the point at which nickel is said to lose its magnetism. In such
inquiries as these the graphical method is almost invaluable, and little
can be expected without its aid.

In applying the formula to this curve, we do not find so good an
agreement as at the lower temperature. I do not consider this conclu-
sive that the formula will not agree with observation at this tempera-
ture; for I have noticed that the curves of different specimens of iron
and nickel seem to vary within a minute range, not only in their
elements but also in their form. This might perhaps be accounted for
by some small want of homogeneity, as in the case of burning in iron
and nickel; but at present the fact remains without an explanation.
But the amount of the deviation is in all cases very small when all the
precautions are taken to insure good results. The nature of the devia-
tion is in this case as follows : when the constants in the formula are
chosen to agree with the observed curve at the vertex and at the two
ends, then the observed curve falls shghtly below the curve of the
formula at nearly all other points. In a curve plotted about 5 inches
high and broad, the greatest distance between the two curves is only
about of an inch, and could be much reduced by changing the con-
stants. For the benefit of those who wish to study this deviation, I
have calculated the following values, which will give the curve touching
the vertex and the two ends of the observed curve of Table III. They
are to he used by plotting in connection with that Table.

tCm

—140

8802

13.75

305

28 SS

18-75

465

2369

33-5

70S

18S5

1306

; 3H-25« + 140

I have not as yet obtained a complete curve of iron at a high temper-
ature; hut as far as I have tried, it does not seem to he affected much,
at least for high magnetizing-powers. I have, however, found that the
maximum of magnetization of iron decreases about 2 per cent by a

Magnetic Pekme ability of Nickel and Cobalt

rise of temperature from 15® C. to C., while that of nickel de-
creases 22 ‘7 per cent.

The experiments which I have made with cobalt do not seem to be
so satisfactory as those made with nickel and iron. There are some
things about them which I cannot yet explain; but as they are the only
exact experiments yet made on cobalt^ they must possess at least a
transient value. The diKiculties of getting a good cobalt-curve are
manifold, and are due to the following properties — (1) its small permea-
bility, (2) its sensitiveness to temperature, and (3) its property of having
its permeability increased by rise of temperature at all magnetiring-
powers within the limits of experiment. The following are the results
with No. I: —

TABLE IV.

CA.8T Cobalt, Nokmal, at 6° C.
Experiments made November S7, 1878.

4b.

IC.

Ob-

Oalou-

Error.

served.

lated.

49-88

4808

87-24

8703

601

888-5

6-86

6.75

— 11

58 -BS

6608

96-82

4526

1082 j

441-6

7-51

7-44

— 07

76-47

8409

100-96

6175

2284

668-1

8-67

8-79

-12

98-16

11638

124-8

7826

8797

917-6

9-86

0-81

— 04

118-0

14998

183-7

9806

5188

1198*1

10-48

10-44

--04

120-8

17439

184-9

10580

6859

1887-8

10-66

JO-73

•06

159-4

22809

140-0

14090

8219

1775-8

11-06

11*00

— 06

189-0

26769

141-6

16260

10609

3180-8

11-19

10*97

— 22

219-6

80680

189-8

18200

13880

3488-5

11-01

10*88

— 18

264 -r

86625

184-2

21120

14406

3827-0

10-60

10*50

— 10

851-1

48421

138-7

36670

17751

8465-0

9-76

9*78

— 08

400-0

46640

110-6

27H80

18810

8711-6

9-20

9-84

•14

552-1

56410

100-4

84090

21820

4409-0

7-91

8-16

•26

782-1

68400

80-6

89850

38650

6045*0

6-81

6-98

•13

999-8

71800

71-8

47810

344i)0

5714-0

6-68

5-55

— 08

1471

80770

54-0

56870

34900

6480-0

4-29

8-98

-•81

8160

TABLE V.

Cast Cobalt, Magi^btio, at —5® C.
Experiments made November 28, 1878.

-b-

48.47

8703

76-87

8287

415

290-8

6*00

76-74

7254

94-54

5760

1494

671*1

7-44

112*8

14870

127-6

9888

4982

1184*5

10-06

167*6

24180

144-0

14490

9640 1

1907

11-88

264*2

86860

186-7

20430

16440

2888

10-72

689*9

58940

99*91

88010

20980

4249

7-87

1478

80760

54*84

55930

24840

6810

4-28

HENaT A. Rowland

TABLE VI.

Cast Cobalt, Magnetic, at *280® O.
Experiments made February 3, 1874.

».*

18-84

1867

101-8

1166

192

107

8-02

25-67

2916

118-6

2662

254

280

8-96

88-66

4940

128-2

4897

648

890

10-12

65-66

9400

169-1

7440

1960

748-6

18-88

76-16

16800

210-2

10060

6760

1148

16-65

101-4

28920

285-9

14260

9660

1895

18-70

182-7

81260

286-5

17710

18650

2476

18-66

172-9

88060

220-2

21820

16240

8015

17-44

281-8

52620

186-4

81160

21860

4174

14-76

898-6

68480

161-2

89070

24860

5089

12-76

702-9

82070

117-0

64920

27160

6615

9-27

989-8

95600

96-68

66760

28850

7684

7-67

1282

106200

82-87

76820

80880

8422

6-67

JProm Table IV we see that at ordinary temperatures cobalt does not
oflEer any exception to the general law for the other magnetic metals —
that as the magnetisation increases, the magnetic permeability first
increases and then decreases. We also see that the results satisfy to a
considerable degree of accuracy the equation which I have used for the
other magnetic metals. The departure from the equation is of exactly
the nature that can be accounted for in either of two ways —either by
the heating of the ring by the current for the higher magnetizing-
forces, or by some want of homogeneity in the ring. According to the
first explanation, the maximum of magnetization at 0® 0. will bo some-
what lower than the curve indicates; but by the second it must be
higher. I, however, incline to the first, that it is due to heating, for
two reasons: first, it is suflBcient; and secondly, the smaller cobalt ring
gives about the same maximum as this. Hence wo may take as th<'.
provisional value of the maximum of magnetization of cobalt in round
numbers 3 = 8000, or S3 = 100,000.

We also see from Table IV that, at least in this case, the permeability
of cobalt is less than that of nickel, though we could without doubt
select specimens of cobalt which should have this quality higher than a
given specimen of nickel. Tlie formula at the foot of tho Table also
shows, by the increased value of the coelTidont of k in th(» right-hand
member, that the diameter of the curve is much less ineliiKMl to tlu^
axis of 3 in this case than in tho cavso of nickel or iron. In this re-
spect the three metals at present stand in the following order — eohali,
nickel, iron. This is the inverse order also of their permea!)ility; hut

Magnetic Pbkmeabilitt op Nickel and Cobalt

at present I have not found any law connecting these twoy and doubt
if any eaact relation exists, though as a general rule the value of the
constant is greater in those curves where the permeability is least.

In a short abstract in the ^Telegraphic Journal/ April 1, 1874:, of a
memoir by M. Stefan, it is stated that the resistance of iron and
nickel to magnetization is at first very great, tlien decreases to a mini-
mum value, which is reached when the induced magnetic moment is
become a third of its maxinmm.^^ This will do for a very rough approx-
imation, but is not accurate, as will be seen from the following Table
of this ratio from my own experiments: —

Experiments published In August, 187a

Iron.
Tables I
and 11.

Iron.
Table III.

Bessemer
steel.
Table IV.

Iron.
Table V.

Nickel.
Table VI.

Steel.
Table VII.

8*08

2*64:

2*65

8-15

S-46

Experiments of present paper.

Kflok^.

Nickel.

Oobalt.

Tables I and IT.

Table HI.

Tables IV and T.

8*14

Ts"

The aTerage of these is, if we ineliide Bessemer steel with the iron, as
it is more iron than steel: —

-/fg = ji ; Nickel, ^ ; Cobalt, .

Hence the place of greatest permeability will vary with the kind of
metal. From these, however, we can approximate to the value of b in.
the formula; for we have

for Iron, b = j for Nickel, b = ;

p P

for Cobalt, 5 = 86,000.

In Table V we have the results for cohalt in the magnetic state.
We here find the same effect of magnetization as we have before found
for iron and nickel.

Hbnbt a. Eowlan-d

In Table VI we have results for cobalt at a high temperature, and
see how greatly the permeability is increased hy rise of temperature,
this being for the vertex of the curve about 70 per cent. But on plot-
ting the curve I was much surprised to find an entire departure from
that regularity which I had before found in all curves taken from iron
and nickel when the metal was homogeneous. At present I am not able
to account for this, and especially for the fact that one of the measure-
ments of SB is higher than that which we have taken for the maximum
of magnetization, at, however, a lower temperature. The curve is
exactly of the same nature as that which I have before found for a
piece of nickel which had been rendered unhomogeneous by heating
red-hot, and thus burning the outside. The smaller cobalt ring gives
a curve of the same general shape as this, but has the top more rounded.
I will not attempt without fresh experiments to explain these facts, but
will simply offer the following explanations, some one of which may be
true. Rrst, it may be due to want of homogeneity in the ring; but it
seems as if this should have ajffected the curve of Table IV more.
Secondly, it may be at least partly due to the rise in temperature of the
ring at high magnetizing-powers; and indeed we know that this must
be greater in paraffin than in alcohol for several reasons : there is about
twice as much heat generated in copper wire at 230® 0. as at 0® with
the same current; and this heat will not be conducted off so fast in
paraffin as in alcohol, on account of its circulating with less freedom;
it probably has less specific heat also. Thirdly, it may be due to some
property of cobalt, by which its permeability and maximum of magneti-
zation are increased by heat and the curve changed.

The experiments made with the small ring confirm those made with
the large one as far as they go; hut as it was so small, they do not
possess the weight due to those with the larger one. But, curious as
it may seem, although they were turned from the same button side hy
side, yet the permeability of the larger is about 45 per cent greater than
that of the smaller. I have satisfied myself that this is due to no error
in experiment, but illustrates what extremely small changes will affect
the permeability of any metal.

We have now completed the discussion of the results as far as th(‘y
refer to the magnetic permeability, leaving the discussion of the tem-
porary and permanent or residual magnetism to the future, although
these latter, when discussed, will throw great light upon the nature
of the coercive force in steel and other metals. The wholes subject
seems to be a most fruitful one, and I can hardly understand why it has

Ma-O-netio Pbrmbabilitt or Niokbli and Cobalt

been so much neglected. It may have been that a simple metbod of
experiment was not known; but if so, I believe that my method will be
found both accurate and simple, though it may be modided to suit the
circxunstances. Professor Maxwell has suggested to me that it would
be better to use rods of great length than rings, because that in a ring
we can never determine its actual magnetization, but must always con-
tent ourselves with measuring the change on reversing or breaking the
current. This is an important remark, because it has been found by
MM. Marianini and Jamin, and was noticed independently by myself
in some unpublished experiments of 1870, that a bar of steel which has
lain for some time magnetized in one direction will afterwards be more
easily magnetized in that direction than in the other. This fact could
not have been discovered from a ring; and indeed if a ring got a one-
sided magnetism in any way we might never know it, and yet it might
affect our results, as indeed we have already seen in the case of the
magnetic curve. But at the same time I think that greater errors
would result from using long bars. I have tried one of iron 3 feet
long and i inch diameter; and the effect of the length was still appar-
ent, although the ratio of length to diameter was 144. To get exact
results it would probably have to be several times this for the given
specimen of iron, and would of course have to be greater for a piece
of iron having greater permeability. This rod must be turned and
must be homogeneous throughout — conditions which it would be very
difficult to fulfil, and which would be impossible in the case of nickel
and cobalt. We might indeed use ellipsoids of very elongated form;
and this would probably be the best of all, as the mathematical theory
of this case is complete, and it is one of the fow where the magnetization
is uniform, and which consequently will still hold, althotxgh the portnea-
hility may vary with the amotmt of magnetization. This form will, of
course, satisfy Professor Maxwell’s objection.

The method of the ring introduces a small error which has never
yet been considered, and which will affect Dr. Stolctcw’s results as well
as mine. The number of lines of induction passing across the circular
section of a ring-mngnot wo have seen to he

' a?

in vhich a is the mean radius of the ring, B the radius of the section,
n' the number of coils in the helix, and i the intensity of the enrrent-
NTo'w" in integrating this before, I assximed that (jl 'wb.b a constant
throughout the section of the ring: now we have found that ft is a

Hbnby a. Eowland

fimctioii of the magnetization, and hence a function of the magnetizicig“
force; hnt the latter varies in different parts of the section, and hence
fi mnst vary. Bnt the correction will be small, because the average
value will be nearly the same as if it were a constant. We may estimate
the correction in &e following manner. Let [x and § be the valnes of
those quantities at any point in the section of the ring, fj! and the
valnes at the centre of the section, and /x, and the observed values.
Then, by Tayloris theorem,

But $ = and , and bo we have

But in my Tables I have already calculated

and aB fi^ is very nearly equal to fif, and §,to we have approxitnately
a'-a ^ ^ +&c)

^ V 'Si 3®; IT + T ■?“ + ®°’j

\ 4 €1^ j j

which will give the value of fJ corresponding to and Hence the
correct values of the quantities will be //, and S'=§V.

The quantities and can he obtained either by measuring a
plot of the curve, or from the empirical equation
;. = Bsin'iS_+5iL±.5,

when we know the values of the constants. In this case
diJ- u ft — A/

d^, ~ ^ ’

(aB» - 3 m?) t ft?(§, + J) V - mT
m O'

in which

0 = 57-3Z> T (^ + 5) V 5*'- 4 .

Magnetic Pebmeabilitt or NiokbIi and Cobalt

In all these the upper signs are to he taken for all values of ^^less than
and the lover signs for greater values.

On applying these formulae to the observations, I have fonnd that the
corrections ■will in no •way influence my conclusions, being always very
small; but at the same time the calculation shows that it would be well

to diminish the ratio -- as much as possible. In all my rings this ratio

did not depart very much from ^ ; b'ut I would advise future experi-
menters to take it at least as small as the amount of correction

will he very nearly proportional to the square of — .

Summary.

The foUoving laws have been established entirely by my own experi-
ments, though in that part of (8) which refers to iron I have been
anticipated in the publication by Dr. Stoletow (PhiL Mag. Jan. 1873).
When «my measurements are given, they are on the metre, gramme,
second system.

(1) Iron, nickel, and cobalt, in their magnetic properties at ordinary
temperatures, differ from each other only in the quantity of those
properties and not in the quality.

(2) As the magnetizing-force is increased from 0 upwards, the resist-
ance of iron, nickel, and cobalt to magnetization decreases until a
minimum is reached, and after that increases indefinitely. This mini-
mum is reached when the metal has attained a magnetization of from
•24 to -38 of the maximum of magnetization of the given metal.

(8) The curve showing the relation between the magnetization and
the magnetic permeability, or ITeumaim's coefficient, is of such a form
that a diameter can he drawn bisecting chords parallel to the axis of 0,
and is of very nearly the form given by the equation

fi = Bain ,

where and D are constants, // is the ratio of the magnetization to
the magnetizing-force in an infinitely long bar, and 0 is the amount
of magnetization.

(4) If a metal is permanently magnetized, its resistance to change of
magnetism is greater for low magnetizing-powers than when it is in the
normal state, hut is the same for high magnetizing-powers. This

Henky a. Rowland

applies to the pennaneat state finally attained after several reversals of
magnetizing-foTce; but if we strongly magnetize a bar in one direction
and then afterwards apply a weak magnetizing-force in the opposite
direction, the change of magnetization will be very great.

(5) The resistances of nickel and cobalt to magnetization vary with
the temperature j but whether it is increased or not in nickel depends
upon the amount of magnetization : for a moderate amount of magneti-
zation it decreases with rise of temperature very rapidly; hut i£ the
magnetization is high the resistance is increased. In cobalt it appar-
ently always decreased, whatever the magnetization. The resistance
of iron to magnetization is not much affected by the temperature.

(6) The resistance of any specimen of metal to magnetization de-
pends on the kind of metal, on the quality of the metal, on the amount
of permanent magnetization, on the temperature, and on the total
amount of magnetization, and, in at least iron and nickel, decreases
very much on careful annealing. The mammum of magnetization
depends on the kind of metal and on the temperature.

(7) Iron, nickel, and cobalt all probably have a maxunum of magneti-
zation, though its existence can never be entirely established by experi-
ment, and must always be a matter of inference; but if one exists, the
values must be nearly as follows at ordinary temperatures. Iron when
S5 = 175,000 or when 3 = 13,900; nickel when S5 =63,000 or when
3[ = 494:0; cobalt when S8 = 100,000( ?) or when 3 = 8000 (?).

(8) The maximum of magnetization of iron and nickel decreases with
rise of temperature, at least between 10® 0. and 220° C., the first very
slowly and the second very rapidly. At 220® 0. the maximum for iron
is when 8 = 172,000 and 3 = 13,600, and for nickel when 8=49,000
and 3 = 3800.

The laws which govern temporary and residual magnetism, except so
far as they have been hitherto given, I leave for the future, when I
shall have time for further experiment on the subject to develop some
points which are not yet quite clear.

2Vo2/, YorTc^ V. S. JL., Aprils 1874.

OF A NEW DIAMAG-NETIC ATTACHMENT TO THE LANTERN,
WITH A NOTE ON THE THEORY OF THE OSCILLATIONS
OF INDUCTIVELY MAGNETIZED BODIES

[JimeHem Tournal of tkiettce [3], IX, 857-861, 1876]

1. Desokiption op Appabaots

Some time ago, in thinking of the theory of diamagnetism, I came
to the conclusion that apparatas of large size was by no means neces-
sary in diamagnetic experiments, and on testing nay conjectures experi-
mentally, I was much pleased to find that they were true. So that for
more than a year I have been in the habit of illustrating this subject
to my classes by means of a small apparatus weighing only about a
poimd or two, which I place in my lantern and magnify to a large size
on the screen.

The effects obtained in this way are very fine and are not surpassed
by those with the largest magnets; and we are by no means confined
to strongly diamagnetic substances, but, with proper care, can use any-
thing, even the most feeble. The apparatus which I used consisted of
a horseshoe cleetro-magnct, made of an iron bar half an inch in diam-
eter and about ten inches long, bent into the proper form, and sur-
rounded with four or five layers of No. 1C wire. But the following
apparatus will, without doubt, be found much more couvoniont. It can
be made of any size, though the dimensions given will probably be
found convenient.

FiGcrua 1.

The apparatus is ropresentod in Fig. 1. To a straight bar oi iron fc,
7 in. long, J in. thick, and f in. wide, are attached two pieces e e oi
the same kind oi iron by two set screws g g, which naove in slots in the

Hbnet a. Howland

piece h. Into these pieces axe screwed two tubes c made of iron and
having an internal diameter of about in. and a thickness not to
exceed ^ in. Through these tubes the iron rods a 6 slide and are
held at any point by the screws A. One end & of this rod is rounded
off for diamagnetic experiments and the other enlarged and flattened
at the end for magnecrystallic experiments. On the tube c a helix of
No. 16 or No. 18 wire is wound so as to make up a thickness of -4 or *5
of an inch and having a length of in. The object of the screws g is
principally to allow the rods a b to be reversed (quickly and to adjust the
position of the helices. When the apparatus is to be used for only one
kind of work it can be much simplified by doing away with many of the
moving parts.

This instrument can be used either with the ordinary magic lantern,
or better, with one having a vertical attachment. In the latter case
the plane of the instrument is horizontal and the substances are sus-
pended from a wire made quite small, so as not to cut off too much
light.

The suspending thread in the case of bismuth can be quite large
but for other bodies a single fibre of silk is best; these in the shape of
bars half an inch long can be each attached to a fibre »having a little
wire hook at its upper end and hung in a cabinet until required.

The theory of feebly magnetic or diamagnetic bodies oscillating in
a magnetic field is very simple and yet the results are of the greatest
interest, especially the effect of the size of the apparatus, which is
here given for the first time.

2. Thbout

Let a very small particle of a body whose coefficient of magnetization
#c is very small, and either positive or negative, be placed in a magnetic
field of intensity R; it will then have an induced magnetic moment of
K'vRy where v is the volume of the element. The force acting on this
particle to cause it to go in any given direction will be equal to the
product of the magnetic moment into the rate of variation of B in that

direction,^ and hence is kvR^^ in the direction of x. The total force

acting on the body in the direction of x is therefore

> ThomBon, Eeprint of Papers, art. 679, Prob. vll.

New Dxakagnetio Attaohmeht to the Lanxebn

aiid the other componeEts of the force are

aad

J S'"

Let, now, the axis of z he vertical, the axis of sc ia the line of the
magnetic poles of the magnet, and y at right angles to both. Then
the moment of the forces acting on tiie body to turn it about the axis

where the integration extends throughout the volume of the body.

If the body is suspended so as to turn freely about the axis of z it
will vibrato about the position for which Jlf is a minimum or else will
remain at rest at that point. The number of single oscillations made
when the angular elongation ■» is very small, is

n =

1 / M

~v 51 ’

in. which M and # must be measured simultaneously, and I is the
moment of inertia of the body.

How let UH suppose that the whole apparatus changes size, the relation
between tlio parts remaining constant, so that the apparatus becomes
m times as great as before. Then sc, y, dx, dy, and dz will increase m

times and I, m® times. To determine the changes in ^ and

we make use of the theorem of Sir Wm. Thomson, that “ similar bars
of different dimensions, siinilai-ly rolled, with lengths of wire propor-
tional to the squares of their linear dimensions, and carrying equal
currents, cause equal forces at points similarly situated with reference
to them.” But as the above only applies to equal currents, I have
generalized it in the following: In any two magnetic systems whatever,
simlar in all their parts and composed of any numher of permanent or
electro-magnets, wires carrying currents, or bodies under magnetic induc-
tion, the magnetic force at similar points of each will be the same when the
following conditions are complied with: let, the magnetic materials at
similar points in the two systems must be exactly die same in quality and

Hbnet a. Eowland

temper; M, the permanent magnets must le magnetized to the same degree
at similar points of the systems j Sd^ the coils of the electro-magnets and
other wires or lundles of wires carrying the current must have similar
external dimensions in the two systems and must have the product of the
current hy the number of wires passing through similar sections of the two
systems proportional to the linear dimensions of fhe systems.

This mil apply to the case we are considering when the product of
the current by the number of the turns of wire varies in direct propor-
tion to the size of the apparatus. Hence in this case

will vary inversely as m. Hence we see that n will be inversely pro-
portional to the size of the apparatus; and although we have only
proved this for the case when k is small, it is easy to see that it is
perfectly general. The advantage of small diamagnetic apparatus is
thus apparent, for the smaller we make it the more Vibrations the bar
will make in a given time and the more promptly will the results be
shown.

It might be thought that by hanging a very small bar in the field of
a large magnet, we might obtain just as many vibrations as by the use
of a small apparatus; but this is not so, for Sir Wm. Thomson has
shown * that the number of oscillations of a feebly magnetic or diamag-
netic body of elongated form in a magnetic field is nearly independent
of the length when that is short. So that the only way of increasing
the number of vibrations is to decrease the size of the whole apparatus,
or to increase the power of the magnets; the latter has a limit and
hence we become dependent on the former.

The theory of the effect of the size of the body is very simple, and we
may proceed as follows. Let the body be in the form of a small bar
whose sectional area, a, is very small compared with its length, and let
X be the angle of the axis of the bar with the line joining the poles, and
r the radius vector from the origin. Developing as a function of
X and y by Taylor^s theorem, and noting that as R is symmetrical with
reference to the planes XZ and FZ, only the even powers of x and y
can enter into the development, we have, calling R^ the value of 7?
at the origin,

a? +

Reprint of Papers, art. 670. Bemarques sur les oscillations (raiguilles non crys-
tallis^es.

New Diamagnetic Attachment to the Lantbbn

79 '

Whea thie vibrating body is very small the first two terms will suffice :
hence we have

in which I is the length of the bar. If $ is the density of the body

/y 78 A

(weight of a unit of volume), 1= - and n becomes

in which, however, it is to be noted that is essentially negative

and so the sign of the term containing it will be positive in the actual
development.

This equation is independent of the dimensions of the body, and
hence we conclude that when the body is small and very long as com-
pared with its other dimensions, the number of vibrations which it will
make in a given field is dependent merely on its coefficient of magneti-
zation and on its density; a result first given by Sir Wm. Thomson, in
the paper referred to. I have given it once more and put it in its
present form merely to call attention to the facility with which * can
be obtained from it when we have measured B in different parts of the
field by known methods. This could be done by means of a rotating
coil as used by Verdet, or by my magnetic proof plane which I will
soon describe, combined with my method of using the earth inductor.
This will give the best method that I know of for obtaining * for
diamagnetic or weak paramagnetic substances.

2Voy, Jcmvarp 16, 1875.

NOTES ON MAGNETIC DISTRIBUTION

iProeetdfingt of the American Academy of Arts and Sciences, XI, 191, 192, 1876. Vre-

Bented June 9, 3 875]

In two papers which have recently appeared on this subject, by Mr.
Sears (Amer. Jour, of Science, July, 1874), and Mr. Jacques (Proc.
Amer. Acad, of Sciences, 1876, p. 445), a method is used for determining
magnetic distribution, founded on induced currents, in which results
contrary to those published by M. Jamin have been found. It does not
seem to have been noticed that the method then used does not give
what we ordinarily mean by magnetic distribution. In mathematical
language, they have measured the surface integral of magnetic induc-
tion across the section of the bar instead of along a given Ungfh of its
surfaced M. Jamin’s method gives a result depending on the so-called
surface density of the magnetism, which is nearly proportional to the
surface integral of the magnetic induction along a given length of the
bar. Hence the discrepancy between the different results. Had the
experiments of Mr. Sears and Mr. Jacques been made by sliding the
helix inch by inch along the bars, their results would have confirmed
those of M. Jamin. Four or five years ago, I made a large number of
experiments in this way, which I am now rewriting for publication, and
where the whole matter will be made clear. At present, I will give the
following method of converting one into the other. Let Q be the sxir-
face integral of magnetic induction across the section of the rod, and

let Qe be that along one inch of the rod: then Qe oc being the

distance along the rod. Hence, M. Jamin’s results depend on the rate
of variation of the magnetization of the rod, while those of Mr. Soars
and Mr. Jacques depend on the magnetization. In conclusion, lot mo
heartily agree with Mr. Jacques’s remarks about M. Jamin’s conclusions
from his experiments. Such experiments as those give no data what-
ever for a physical theory of magnetism, and can all be deduced from
the ordinary mathematical theory, which is independent of physical

‘Uaxwell’s Electricity and Magnetism, art. 402.

KToxes on Maqnbxio Dibteibuxion’ 81

lypothesis, combined with what is known with regard to the magnetiz-
ing fnnction of iron. This will be shown in the paper I am rewriting,
[t seems to me that M. Jamin’s method is very defective; and I know
of no method of experimenting, which is theoretically without objection
except that of induced currents, and this I have used in all my experi-
ments on magnetic distribution for the last four or five years, and have
developed into a system capable of giving results in absolute measure.
Mr. Jacques is to he congratulated on pointing out these errors in
M. Jamin’s conclusions.

Troy^ Jhme 7 , 1875 .

NOTE ON KOHLEAUSCH’S DETBEMINATIGN OF THE ABSO-
LUTE VALUE OF THE SIEMENS MEBOUEY UNIT OF
ELEGTEIOAL EESISTANCE

{Philotophical 2£agazi/M [4], J&, 101-163, 1876]

In looking over Kohlransch’s paper* upon tke determination of a
resistance in atsolute measure, with a view to undertaking sometliing
of the kind myself, and also, if possible, to discover the reason of the
difference from the results of the Committee of the British Association,
I I have come across an error of sufficient magnitude and in the
proper direction to account for the 3 per cent difference. Kohlrausch’s
experiments were made with such great care and hy so experienced a
person that it is only after due thought and careful consideration that
I it upon me to offer a few critical remarks.

We observe, then, first of aH, that the principal peculiarity of his
method consists in doing away with all measurements of the coils of
the galvanometer, and in its place making accurate determinations of
the logarithmic decrement both with the circuit closed and open, to-
gether with various absolute determinations rendered necessary by this
change. In this way the logarithmic decrement is raised from being a
fl-mgll correction to a most important factor in the equation. TToncc
it is that we should carefully scrutinize the theory and see whether it
be correct enough for this purpose ; for only an approximation is ncodiMl
for the first method.

The resistances to a bar magnet swinging within a coil may be divided
into two principal parts — first, that due to the resistance of air and
viscosiiy of suspending fibre, and, second, that due to the induced cur-
rent in the coils. The first resistance is usually taken as proportional
to the velocity, and thus assumes the viscosity of the air to be the most
important element. This is probably true in moat oases where ihe
motion is slow. This factor is quite small compared with the second
when the magnet is large and heavy and the coils wound close to it, as

'Poggendorll’s Ergilnzungsband vl, p. 1; translated In I'hll. Mag., S. I,

vol. xlvii, pp. 294, 842.

Note on Kohlkausoh^s Determination

in Kohlrausch's instrument. Kohlrauscli^s principal error lies in the
omission of the coefficient of self-induction from his equations.

For the sake of clearness, and because the subject is quite often
misapprehended, I shall commence at the beginning and deduce nearly
all equations.

Let us proceed at first in the method of Helmholtz, using the nota-
tion of Maxwell’s ' Electricity.^

Let a current of strength I be passing in a circuit whose resistance
is 7?, and coefficient of self-induction L, Also let a magnet be near the
circuit whose potential energy with respect to the circuit is IF. Let A
be the electromotive force of the battery in the circuit.

The work done by the battery in the time dt is equal to the sum of
the work done in heating the wire, in moving the magnet, and in
increasing the mutual potential of the circuit on itself,^ Hence we have

Aldt = PJiclt + l^dt + -i- L dt)
dt a dt ’

and if /I is oqnal to zero, vc find

1 (dV
E\dt.

+ L

If we apply this to the case of a magnet swinging within a coil the
angle of the magnet from a fixed position being x, we have since

is the moment of the force acting on the magnet with unit current and
may be denoted by q,

where my li is KohlrauHch^s w.

This expression differs from that used by Kohlrausch in the addition
of the last term, which is the correction duo to self-induction. The
last term vanishes whimcvor the magnet moves with such velocity as
to keep the induced current constant; but in the swinging of, a gjilvano-
meter-ncedlo it has a value.

To form the equation of motion of the needle, wo can proceed the
rest of the way as Maxwell has done (Electricity, art. 7GS). Assuming
that all frictional resistances to the noodle are proportional io the
velocity of the needle, we have

where //, (\ and 1) are constants.

2*See remarks in MaxwolPfl ‘Electricity,’ art. 644, near bottom o£ page.

Hbnet a. Bowland

Blimiiiating I between this equation and (1), we find

At first sight this equation will appear to be the same as that of Max-
well; but on further examination we see that it is more general in the
value of q-

Equation (3) is the correct equation to use in this case^ and reduces

to that of Kohlrausch when L = 0.

To see how this error will afEect Kohlrausch^s results, we must re-
member that he uses this equation to find the constant of his galvano-
meter, on which his whole experiment depends; and the error is so
interwoven with all his results that an entire recomputation is neces-
sary, provided the data for calculating the coefficient of self-induction
of the galvanometer coils and earth inductor can be obtained.

The equation

f _ fo
^ + 7r» + A?

does not hold when self-induction is considered; and so his fundamental
equation (1) is not correct, containing a twofold error.

The linear differential equation (3) is easily solved; but as the results
are complicated, it is hardly worth while at present, until a recalcula-
tion can be made. I prefer to solve it on the supposition that L is
small, and thus merely obtain a correction to Eohlrausch^s equation
connecting t and after which equation (15) or (17) (MaxwelFs ' Elec-
tricity,^ art. 762) can be used when made more general by substituting
q for Qm.

As far as I have had time to go at present, the correction seems to
be in the direction of making KohlrauscFs determination more nearly
coincide with that of the Committee on Electrical Standards of the
British Association. Other engagements occupy my attention at pres-
ent; but I hope to see these corrections made to an otherwise excelletii
determination of this most important unit.

London^ Avg'tut 4, 1875.

PEELIMINARY NOTE ON A MAGNETIC PROOF PLANE

[Amerioan Journal of Soienee [8], X, 14-17, 1875]

About tour yeaxs ago I made a large number of ezperimeutB on the
distribution of magnetism on iron and steel bars by means of a coil of
we sliding alqng the bar; the induced current in the coil as measured
by a galTanometer was a measure of the number of lines of force cut by
the coil and can be found in absolute measure by my method of using
the earth inductor. These researches have never yet been published
owing to circumstances beyond my control, but are known to quite a
number of persons in this country, and will soon be published. The
method there used is the only correct one that I know of for experi-
menting on magnetic distribution, and my purpose in this note is to
extend it to bodies of aU shapes, so that experiments on magnetic dis-
tribution may become as simple and easy to perform as those on elec-
trical distribution. And so well has my magnetic proof plane accom-
plished this that I can illustrate the subject to my classes with the
greatest ease.

The apparatus required is merely a small coil of wire i to ^ inch in
diameter, containing from 10 to 60 turns, and a Thonoson galvanometer.
When we require to reduce to absolute measure, another coil about a
foot in diameter and containing SO or 30 turns is required. Having
attached the small coil (or, as I call it, the magnetic proof plane) to
the galvanometer, we have merely to lay it on the required spot, and
when everything is ready, to pull it away suddenly and carry it to a
distance,, and the momentary detection of the galvanometer needle will
be proportional to that component of the lines of force at that point
which is perpendicular to the plane of the coil. And if we apply it to
the surface of a permanent magnet the so-called surface density of the
magnetism at that point will be nearly proportional to the deflection.
In the case of an electro-magnet the surface density will be nearly pro-
portional to the deflection minus the deflection which would be pro-
duced by the helix alone, though the last is generally small and may be
neglected. I use the words nearh/ proportional in the above statement
because they are only exactly true in the cases where the lines of force

Hbnbt a. EowiiAnd

proceed from tie surface iu a perpendicular direction; otierwise the
defl-ections must he multiplied by the secant of the angle made by the
linaa of force mth the surface of the magnet. In the case of an electro-
magnet made of very soft iron, theory shows that the lines pass out
nearly perpendicular to the surface and so no correction is needed.

We can also, by a coil of this kind, determine the intensity of the
magnetic field at any point and thus be able to make a complete map
of it. Having done this, we have all the data necessary to substitute
in the formula which I have given in this Journal,* and by a simple
experiment can thus determine the coefficient of magnetization of any
■diamagnetic or weak paramagnetic body probably in a more accurate
manner than any Weber used. Only the largest-sized magnets could of
course be used for this purpose with any accuracy, and indeed' they arc
always to be preferred in obtaining the distribution by this method.

Having obtained the distribution for any given magnet, the distribu-
tion for any similar magnet of the same material but of different size
becomes known by a well-lcnown law of Sir William Thomson.

As, in the present state of our Imowledge, magnetic measurements
are of small value unless made on the absolute scale, we require to
reduce our results to this system. There are several methods of doing
this, but the simplest is that which I have used in my experiments on
magnetic permeability, and consists in including an earth inductor in
the circuit. A coil laid on a perfectly level surface is sufficient for
this : when this is turned over, the induced current will be equal to 0 =

where n is the number of turns in the coil, A its mean area, T

the veirtical component of the earth’s magnetism, and 2? the resistance
of the circuit. When the small coil is pulled suddenly away the current

will be (7' = ^, and so we have § = 27^^', in which when a
Thomson galvanometer is used O' and 0 can be replaced by the cor-
responding deflections; hence g = 27-^,^, in which a and n' are the

area and number of turns in the small coil and Q is that component of
the magnetic field we are measuring in the direction of the axis of the
small coil.

As an illustration of this method I will give a few experiments madi*
with the magnets of a Rxihinkorl! diamagnetic apparatus, which was
altogether about 2 ft. long and had its magnets 2 in. in diamoLor, with

iQii anew diamagnetic attachment to the lantern, &ic., this fTournal, May, lK7r>.

Pbeliminaet Note on a Magnetic FttooE Plane

a hole i in. in diameter through them for experiments on the rotation
of the plane of polarization of light, but which in these experiments
were closed by the solid poles which were screwed on. The first experi-
ments were with two discs of iron, 4 -6 in. in diameter and If in. thick,
screwed on to the poles. In the first place the poles were turned away
from one another, the current being sent through only one magnet,
and the values of the magnetic field obtained at different points close to
the surface of the disc. These may be numbered as follows: No. 1, at
centre of face of disc; No. 3, on face of disc half an inch from the edge;
No. 3, on centre of edge of disc. The measures are on the metre, gram,
second system.

1st. Strength of current, 4-4 farads per second.

1. 2330. 3. 3550. 3. 4440.

3nd. Strength of current 8'3 farads per second.

1. 3600. 3. 6300. 3. 7500.

Next the poles were turned toward each other and the current sent
through both magnets, so as to make the poles of the same name.
Current 4‘6 farads per second.

1st. Distance of poles, 8 in.

1. 1300. 3. 3800.

3nd. Distance of poles, 1^ in.

1. 600. 3. 4000.

Hero we see an approach to one of Faraday's places of no magnetic
action.

After this the current in one of ffie magnets was reversed so as to
make the poles opposite. Current the same.

1st. Distance of poles, 3 in.

1. 6800. 2 . 8300. 3. 6700.

3nd. Distance of poles, 1^ in.

1. 9800. 2 . 7500. 3. 6800.

It is curious to note how the distribution changes with the distance of
the discs; thus, on one disc free from the other, the edge of the disc
has the greatest magnetic surface density, but when the two discs form
opposite poles and are 3 in. apart, position. 3 gives the greatest effect,
while, when they are 1^ in. apart, the field is greatest at the cenlro.
This entirely agrees with theory.

The conical poles for diamagnetic experiments were then screwed on.
Those were portions of cones with an angle at vortex of about 60®, with
the vertex considcrahly rounded off. They were one inch apart and
the poles were opposite. Current 4 '4 farads per second.

Hbitrt a. Bo-wiiASTD

At centre of field between the poles

On the axis near one pole

On cone one inch from vertex

On cylindrical portion of magnet 2^ inches from the
vertex of the cone

12600

32100

11000

6800

These poles were now replaced by fmstnms of cones with flat ends,
the original diameter of the iron, 2 inches, being reduced at the end to
l-J inches, and they were placed J inch apart. The field in this case
between them was 61000, or nearly up to the maximiun of magnetiza-
tion of nickel at common temperatures, and above that at high tem-
peratures.

2V4r, 1, 1876.

STUDIES ON* MAGNETIC DISTEIBUTION

iPhilo^ophical Magazine [4], X, 257-277, 848-367, 1876]
iArnericau Journal of Science [8], JST, 826-885, 451-469, 1876; XT, 17-29, 108-108, 18761

Part I. — Linear Distribution
Contents

1. Preliminary remarks,

II. Mathematical theory.

III. Experimental methods for measuring linear distribution.

IV. Iron rods magnetized by induction.

V. Straight electro-magnets and permanent steel magnets.

VI. Miscellaneoas applications.

In a paper of name published about two years ago, I alluded to some
investigations which 1 had made in 1870 and 1871 on the distribution
of magnetism. It is with diffidence that I approach this subject, being
aware of the great mathematical difficulties with which it is surrounded.
But as the facts are still In advance of what is known on the subject,
and as I see that other investigators ' are following hard upon my foot-
steps, I thought it would be well to publish them, particularly as it is
no fault of mine that they did not appear some years ago.’ The mathe-
matical theory which I give, although not particularly elegant, will at
least bo found to present the matter in a new and more simple light,
and may be considered simply as a development of Faraday’s idea of
the analogy between a magnet and a voltaic battery immersed in water.
I shall throughout speak of the conduction of, and resistance to, lines
of magnetic force, and Bliall othorwise treat them as similar to lines of
conducted electricity or heat, it now being well established from the
researches of Professor Maxwell and others that this method gives
exactly the same results as. the other method of considering the action
to take place at a distance.

In arranging this paper I have thought best to give the theory of

1 Particularly M. Jamin.

9 All tbe experiments referred to in this paper were made in the winter of 1870-71.

Henry A. Howland

the distribution first, and then afterwards to see how the results agree
with experiment; in this way we can find out the defects of the theory,
and what changes should be made in it to adapt it to experiment.

At present I am acquainted with two formulae giving the distribu-
tion of magnetism on bar magnets : the first was given by Biot, in Mh
TraiU de Physique Experimentale et MaiMmatique^ vol. iii, p. and
was obtained by him from the analogy of the magnet to a dry electric
pile, or to a crystal of tourmaline electrified by heat.* He compared
his formula with Ooulomb^s observations, and showed it to represent
the distribution with considerable accuracy. Green, in his ‘ Essay,’
has obtained a formiala which gives the same distribution; but he ob-
tains it by a series of mathematical approximations whi'^h it is almost
impossible to interpret physically. M. Jamin has recently used a
formula of the same form; but I have as yet been unable to find how
he obtained it. My own formulae are also quite similar to these, but
have the advantage of being obtained in a more simple manner than
Greenes; and, what is of more consequence, all the limitations are made
at once, after which the solution is exact; so that although they ar<^
only approximate, yet we know just where they should differ from
experiment.

If we take an iron bar and magnetize one end of it either by a magnet
or helix, we cause lines of magnetic induction * to enter that end of the
bar, and, after passing down it to a certain distance, to pass out into
the air and so round to the bar again to complete their circuit. At
every part of their circuit they encounter some resistance, and always
tend to pass in that direction where it is the least: throughout; their
whole course they obey a law similar to Ohm’s law; and the iminlxM*
of lines passing in any direction between two points is equal to th<‘
difference of magnetic potential of those points divided by the r(*sist-
ance to the lines.

The complete solution of the problem before us being impossible, lot
us limit it by two hypotheses. First, let us assume that the ponn(?a-
bility of the bar is a constant quantity; and secondly, that iluj resist-
ance to the lines of induction is composed of two ])arts, the first h<‘iiig
ihat of the bar, and the second that of escaping from the bar into \ho.

3 For ditference between lines of magnetic force and lines of nia^notic induotiou
see Maxwell’s ‘Treatise on Electricity and Ma^ynetisin,’ arts. 400, 5053, and 004.

Studies on Magnetic Dxsteibution

niotliuui ' and that the latter is the same at every part of the bar. The
tirst of these assumptions is the one usually made in the mathematical
theory of magnetic induction; but, as has been shown by the experi-
ments of Miiller, and more recently by those of Dr. Stolotow and my-
self, this is not true; and wo shall sec this when we come to compare
the formula with experiment. The second assumption is more exact
than the first for all portions of the bar except the ends.

Let irs first take the case of a rod of iron with a short helix iilaced on
any portion of it, through which a current ot electricity is sent. The
lines of niagiietic induction stream down the bar on either side: at
every point of the bar two paths are open to them, either to pass further
down the rod, or to pass out into the air. We can then apply the
ordinary equations for a derived circuit in electricity to this case.

Let II be the magnetic permeability of the iron,
li ho the resistance of unit of length of the rod,

W be the resistance of medium along unit of length of rod,
f* be the resistance at a given point to passing down th(». rod,

,s' be th(^ rcsistapc'O at the end of the rod,

(/ ^ he tho number of lines of induction passing along the rod
at a given point,

be tho number of linos of induction passing from Iho rod
into the medium along a small length of the rod
/ibo the distance from the end of the rod to a given point.

To find f), the ordinary equation for tho resistenco of a derived cir-
t‘uit gives

p -H dp =.

whence

Jr:

‘ThOBO arc tho aurfacw-liitn^rttUof ma|?iictIo induction (ho 6 Max^roIUs * Wlootrlclty,’
art. 40Ji)— the llrHt ar.rofls the floctlon of tho bar, anrl the aocond alon^f a length A/;
of tho Burftioc of tlio bar.

is to 1)0 noted tliat whon M is constant, Is nearly proportional to tho so-
called Hurfuoo-denBity of magnetism at the given point.

HBinBT A. Eowujid

, = ( 1 )

To find Q', ve huTe

• dQ!=.^dL,

whence

e' = 3^Me'^+e-"V (2)

and

«'=^f-^=r:^ . . (3)

When L is very large, or 5 we have

^ and ei= CirALe'\

in which is reckoned from an origin at any point of the rod.

These equations give the distribution on the part ontside the helix;
and we have now to consider the part covered by the helix. Let us

limit ourselves to the case where the helix is long and thin, so that the
field in its interior is nearly uniform.

As we pass along the helix, the change of magnetic potential due to
the helix is equal to the product of the intensity of the field multiplied
by the distance passed over; so that in passing over an elementary dis-
tance dy the difference of potential will be ^dy. The number of lines
of force which this difference of potential causes in the rod will be equal
to ^dy divided by the sum of the resistances of the rod in both direc^-
tions from the given point. These lines of force stream down the rod
on either side of the point, creating everywhere a magnetic potential
which can be calculated by equation (2), and which is represented by
the curves in Fig. 1. In that figure A B the rod, C D the helix, and

» This could have been obtained directly from the equation and from

the equation O'* = A h.

Studies on Magnbtio Disteibution

M the element of length, dy. Now, if we take all the elements of the
rod in the same way and consider the effect at R F, the total magnetic
potential at this point wiU, hy hypothesis No. 1, be equal to the sum
of the potentials due to all the elements dy.

Tjet dQ' be the number of lines of force produced in the bar at the
point F due to the elementary difference of potential at
that point, ©dy,

dQ" be the number lines of force arriving at the point F due
to the same element,

Q" be the number of lines passing from bar along length dL,

| 0 , be the sum of the resistances of the bar in both directions
from E,

jr>,be resistance at F in direction of P,
y be the distance P E,

X be the distance P F,
i be the distance 0 P,

s" and s' be the resistance of the bar, &c., xespectiTely at 0 in
the direction of A, and at P in direction of B,

Let

+ /72.

pf =

ifAi-Hrib-y)

RB',

AQf

_ _©

' A'A"e-* — l 4-l)«^dy,

«' = = vj'

A"e’^ — ®~™ MV*''* fc ~™ I r* u™! Ml

This gives the positive part of Q','- To find the negative part,
change x into 6 — x, A' into A", and A" into A', and then change the
sign of the whole.

"When the helix is symmetrically placed on the bar, we have s'=s",
A' =A"; whence, adding the positive and negative parts together, w(!
have

Hbnbt a. Rowland

Q” =

1 — A'

A '®**— 1

(er(»-«) _ e«) J

. • ( 6 )

which gives the number of lines of induction passing out from the rod
along the length JL when the helix is symmetrically placed on the rod.

To get the number of lines of induction passing along the ,rod at a
given point, we have

¥R A'e^ — 1

(f’‘ +1 — 6 ”

where

gi- (» -•) + C'",

( 6 )

^ ~ r (AV* - IX-v/Jn?"— s')

When the bar extends a distance L' out of both ends of the helix, so
that ,

s' = »'>d A' = -

we have

It may be well, before proceeding, to define what is meant by mag-
netic resistance, and the units in which it is measured. If, fx is the
magnetic permeability of the rod, we can get an idea of the meaning
of magnetic resistance in the following manner. Suppose we have a
rod infinitely long placed in a magnetic field of intensity © parallel to
the lines of force. Let Q* be the number of lines of inductive force
passing through the rod, or the surface-integral of the magnetic induc-
tion across its section; also let a be the area of the rod. Then by

definition fjL = ^, If L is the length of the rod, the clifterenco of
potential at the ends will be L© ; hence

and B in the formulas becomes

i2 =

L a/A

It is almost impossible to estimate B* theoretically, seeing that it
will vary with the circumstances. We can get some idea of its nature,
however, by considering that the principal part of it is due to i.he
cylindric envelope of medium immediately surrounding the rod.
resistance of such an envelope per unit of length of rod is

Studies on Magnetic Disteibution

where 2? is the diameter of the envelope, d of the rod, and /i, the permea-
bility of the meditim. But we are not able to estimate D. If, however,
we have two magnetic systems similar in all their parts, it is evident
that beyond a certain point similarly situated in each system we may

neglect the resistance of the medium, and ^ will be the same for the

two systems. Hence R' is approximately constant for rods of all diam-
eters in the same medium, and r takes the form

It is evident that the reasoning would apply to rods of any section as
well as circular.

In Green’s splendid essay (Eeprint, p. Ill, or Maxwell’s ‘ Treatise
on Electricity and Magnetism,’ art. 439) we find a formifia similar to
equation (5), but obtained in an entirely different manner, and applying
only to rods not extending beyond the helix. In the 'Reprint,’ ^
corresponds to my r; and its value, using my notation, is obtained from
the equation

•231863 — 2 hyp. log p -1-2^ = . . . . (8)

where p = ^.

If we make p a constant in this formula, we must have p == S =
constant; hence

which is the same result for this case as from equation (7).

When p in the two formulse is made to vary, the results are not
exactly the same; but still they give approximately the same results for
the cases we shall consider; and since the formula is at the best only
approximate, we shall not spend time in discussing the merits of the
two.

ni.

Among the various methods of measuring linear magnetic distribu-
tion, we find few up to the present time that are satisfactory. Coulomb
used the method of counting the number of vibrations made by a
magnetic needle when near various points of the magnet. Thus, in

Henet a. Eowlaot)

the curve of distributiou most often reproduced from his work, he used
a magnetized steel har 27 French inches long and 2 lines in diameter
placed vertically j opposite to it, and at a distance of 8 lines, he hung
a magnetic needle 3 lines in diameter and 6 lines long, tempered very
hard; and the number of oscillations made by it was determined. The
square of this number is proportional to the magnetic field at that point,
supposing the magnetism of the needle to be unchanged; and this,
corrected for the magnetism of the earth, gives the magnetic field due
to the magnet alone. This for points near the magnet and distant from
the ends is nearly proportional to the so-called magnetic surface-density
opposite the point. At the end Coulomb doubled the quantity thus
found, seeing that the bar extended only on one side of the needle.

It will be seen that this method is only approximate, and almost
incapable of giving results in absolute measure. The effect on the
needle depends not only on that part of the bar opposite the needle,
but on portions to either side, and gives, as it were, the average value
for some distance; in the next place, the correction at the end, by
multiplying by 2, seems to be inadequate, and gives too small a result
compared with other parts. For at points distant from the end the
average surface-density at any point will be nearly equal to the average
for a short distance on both sides, while at the end it will be greater
than the average of a short distance measured back from the end. To
these errors must be added those due to the mutual induction of the
two magnets.

The next method we come to is that which has been recently used
by M. Jamin, and consists in measuring the attraction of a piece of
soft iron applied at different points of the magnet. In this case it
does not seem to have been considered that the attraction depends not
only on the magnetic density at the given point, but also on that around
it, and that a piece of soft iron applied to a magnet changes the distri-
bution immediately at all points, but especially at that where the iron is
applied. The change is of course less when the magnet is of very hard
steel and the piece of soft iron small. Where, however, we wish to
get the distribution on soft iron, it becomes a quite serious difficulty.
Another source of error arises from the fact that the coefficient of
magnetization of soft iron is a fxmction of the magnetization: this
source of error is greatest when the contact-piece is long and thin, and
is a minimum when it is short and thick and not in contact with the
magnet. Hence this method will give the best results when the con-
tact-piece is small and in the shape of a sphere and not in contact with

Studies ok Ma.gkbtio Distbibtjxion

the magnet, and when the method is applied to steel magnets. But
after taldng all these precautions, the question next arises as to how
to obtain the magnetic surface-density from the experiments. Theory
indicates, and M. Jamin has assumed, that tlie attractive force is nearly
proportional to the square of the surface-density. But experiment
does not seem to confirm this, except where there is some distance
between the two bodies, at least in the case of a sphere and a plane
surface, as in Tyndall’s experiments (Phil. Mag., April, 1851). It is
not necessary at present to consider the cause of this apparent dis-
crepancy between theory and experiment; suffice it to say that the
explanation of the phenomenon is without doubt to be sought for in
the variable character of the magnetizing-function of iron. All I wish
to show is that the attraction of iron to a magnet, especially when the
two are in contact, is a very complicated phenomenon, whose laws in
general are unknown, and hence is entirely unsuitable for experiments
on magnetic distribution.

A third method is that used in determining the correction for the
distribution on the magnets in finding the intensity of the earth’s
magnetism. Usually the distribution is not explicitly found in this
case; but it is easy to see how it might be. Thus, one way would be as
follows : — Take the origin of coordinates at the centre of the magnet.
Develop the distribution in an ascending series of powers of v with
unknown constant coefficients. Calculate the magnetic force due to
this distribution for any points along the axis, or else on a line perpen-
dicular to the magnet at its centre. Determine the force at a series of
points extending through as great a range and as near the magnet as
possible. These experiments give a series of equations from which the
coefficients in the expansion can be determined. Other and better
methods of expansion might be found, except for short magnets, where
the method suggested is very good.

The similarity of this method to that used by Gauss in determining
the distribution on the earth is apparent.

A fourth method is similar to the above, except that the lines of
force around the magnet arc measured and calculated instead of the
force.

The last two methods are very exact, but are also very laborious, and
therefore only adapted to special investigations. Thus, by the change
in direction of the lines of force around the magnet, we have a delicate
means of showing the change in distribution, as, for instance, when the
current around an electro-magnet varies.

Hbnby a. Eowland

The fifth method is that used lately in some experiments of Mr.
Sears (American Journal of Science, July, ‘1874), hut only adapted to
temporary magnetization. At a given point on the bar a small coil of
wire is placed, and the current induced in it measured by the swing of
the galvanometer-needle when the bar is demagnetized. It does not
seem to have been noticed that what we ordinarily consider the mag-
netic distribution is not directly measured in this way; and indeed, to
get correct results, the magnetization should have been reversed, seeing
that a large portion of the magnetization will not disappear, on taking
away the magnetizing-force, where the bar is long. The quantity which
is directly measured is the surface-integral of the temporary magnetic
induction across the section of the bar, while the magnetic surface-
density is proportional to the surface-integral of magnetic induction
along a given portion of fhe tar. In other words, the quantity measured

is Q instead of We can, however, derive one from the other very
easily.

The sixth and last method is that which I used first in 1870, and by
which most of my experiments have been performed. This consists in
sliding a small coil of wire, which just fits the tar and is also very
narrow, along the bar inch by inch, and noting the induced current
over each inch by the deflection of a galvanometer-needle. This meas-
ures Q., except for some corrections which I now wish to note. In the
first case, to give exact results, the lines of force should pass out per-
pendicular to the bar, or the coil must be very small. But even when
the last condition is fulfilled errors will be introduced at certain por-
tions of the bar. The error is vanishingly small in most cases, except
near the ends; and even there it is not large, except in special cases;
for at this part the lines of force pass forward toward the end of the
bar, and so the observation next to the end may be too small, while
that at the end is too large. The correction can be made by finding
where the lines of force through the centre of the section of the coil
in its two positions meet the bar. The error from this source is not
large, and may be avoided to a great extent.

One very great advantage in the method of induced currents is the
facility with which the results can be reduced to absolute measure by
including an earth-inductor in the circuit as I have before described
(Phil. Mag., August, 1873). There is also no reaction (except a tem-
porary one) between the magnet and current; so that the distribution
remains unchanged. Hence it seems to me that this method is the
only one capable of giving exact results directly.

Stxtdies on Magnbtio Distbibtjtion

The coils of wire which I used consisted of from twenty to one
hundred turns of fine wire wound on thin paper tubes which just fitted
the bar and extended considerably beyond the coils. The coils were
mostly from -1 to -26 of an inch wide and from •! to -2 inch thick. A
measure being laid by the side of the given bar under experiment, the
coil was moved from one division of the rule to the next very quickly,
and the deflection produced on an ordinary astatic galvanometer noted.
After experience this could be done with great accuracy. It might be
better in some cases to have the coil slide over a limited distance on
the tube, though for the use to which I intend to put the results the
other is best.

Up to 35° is nearly proportional to the deflection; and when any
larger value is put down in the Tables, it is the sum of two or more
deflections. I have not the data in most cases to reduce my results
to absolute measure, but took pains to ensure that certain series of ex-
periments should be comparable among themselves.

Having measured Q, at all points of a rod, we may find Q by adding
up the values of Q, from the end of the rod.

The magnetizing force to which the bar was subjected was in all
cases a helix placed at some part of the bar. The iron bars were of
course demagnetized thoroughly before use by placing them in the
proper position with reference to the magnetic meridian and striking
them.

In the Tables L is the distance in inches from the zero-point, Q , is
the deflection of the galvanometer when the helix is passed between the
points indicated in the first column. Thus, in Table II, 34'7 is the
deflection on the galvanometer when the helix was moved from the
tenth to the eleventh inch from the zero-point; and so we may con-
sider it as tire value of Q, at 10^ inches; so that the values of Q, refer
to the half mches, but Q to the even inches.

In all the calculations the constants in the formul© were taken to
represent Q most nearly, and then the corresponding formulse for Q,
taken with the same constants.

For ease in calculating by ordinary logarithmic Tables, we may put

IV.

Table I is from a bar 174 inches long with a magnetizing helix I 4
inch long at one end, the zero-point being at the other. Table II is
from a bar 9 feet long with a helix 44 inches long quite near one end,
the zero-point being at 1 inch from the helix toward the long end.

100

Henry A. Eowland

Table III is from a bar 2 feet long with a helix 4^ inches long near
one end, so that its centre was 19| inches from the end on which the
experiments were made, the zero-point being at the end.

In adapting the formula to apply to the case of Table I, we may
assume that at the end of the bar s =oo and (7 = 0, which is equivalent
to assuming that the number of lines of induction which pass out at
the end of the rod are too small to be appreciated.

TABLE I.

Ba.e *18 Inch DijLMBTKE. 0 at End op Bak.

served.

CiSbti-

lated.

Error of
Q4.

served.

cSou-

lated.

Error of
Q'.

2.7

8-2

2-0

2*6

8-2

8*7

4*8

5-8

6*5

7-7

0-5

2*4

2*8

8*6

4*8

5*2

6*5

8*0

9*9

0 *

— *1

— *4

— *2

— *1

+ *8
+ -4

2*7

6*9

7*9

10*4

18*6

17*8

21*8

26*9

83*4

41*1

60*6

8*6

6*6

8*6

11*0

18*8

17*8

21*6

26*8

88*8

41*8

51*2

++ 1 1 +++++

oo o

O' =3-60(e-»«-r-»«^).

=r3-60(e = S54(e'^^ + «-• aMZ).

In Table II observations were not made over the whole length of
the rod, and the zero-point was not at the end of the bar. It is evident,
however, that by giving a proper value to s we may suppose the bar to
end at any point. As the rod is very long, expressions of the form

(2'— (7"=(7'e-^^— a" and g;=rC7'e--^

will apply-

In Table II the observations were near the end of the rod, and were
repeated several times. ITeglecting the end of the rod, we have a =oo .

In these Tables we see quite a good agreement between theory and
observation; but on more careful examination we observe a certain law
in the distribution of errors. Thus in Table I the errors of Q' are all
positive between 0 and 8 inches; and this has always been found to be
the case at this part of the bar in all my experiments.

The explanation of this is very simple. In obtaining the formuloe,
we assumed that the magnetic permeability of the bar was a constant

Studies on Magnetic Distbibution

101

table II.

Bab >89 In on Diamutbb. 0 at 1 ihoh vbom; Qbliz.

(f.

served.

('aicu-

lated.

Error of
Q5.

Q'-C".

Ob-

served.

Q'-O".

Calcu-

lated.

Error of
Q'.

71-7

05-2

69*5

58-5

51*2

46-7

48-2

40-0

87*2

84-7

81-7

29-5

25-7

25*5

22-0

21*5

20-0

19-1

82*6

27*5

28*0

18*5

14*5

11*8

76-8

65-8

00-2

55-6

51-2

47- 2

48- 5
40-1
37-0
84*1
81-4
28-9
26*6
24*6
22-7
20-9

19- 8
17-8
81-5

20- 7
22-8
19-4
10-5
14-0

+ *1
+ -7
H-2-0

•f -5
+ -8
+ -1
— -2
— -6
— -8
— -6
+ -9

— -9
+ -7

— -6

— -7
-1-8
—1-0

— .8
— -2
+ -9
+ 2-0
+ 2-7

826-*2

758-5

688-8

628-8

675-8

524-1

477-4

484-2

894-2

357-0

822-8

290-6

261-1

285-4

209-9

187-9

166-4

146-4

127-8

94-8

67-8

44-8

25-8

11-8

902-6

825-9

766-1

689-8

629-5

674-3

623-1

476-0

482-5

892-5

855-6

821-6

290-1

261-2

284-5

210-0

187-8

166-4

147-1

129-4

97-8

71-1

48-6

29-0

12-6

—1-2

+ -7
+ 1-6
+ 1-5
+ -7
-1-0
—1-0
—1-4
—1-7
-1-7
—1-4
— -8
— -6
+ -1

— -9
+ *1

— -6
. 0

+ -7
+ 2-1
+ 8-0
+ 8-8
+4-8
+ 8-2
+ 1-8
-1-2

80-5=983-(10)-'«w“— 80-e.
g' =r088«^o«'w®4X=80-(10)- o«WAL.

quantity; but it has been shown by Dr. Stoletow and myself, independ-
ently of each other, that // increases as the magnetism of the bar in-
creases when the latter is not great. Hence between 0 and 8 inches
the resistance of the bar, B, is greater than at succeeding points, and
hence a less number of linos of induction pass down the bar from 8
towards 0 than would be given by the formula, which has been adapted
to the average value of B at from 9 to 14 inches. In Table II this
same fact shows itself towards the end of the Table, and would prob-
ably bo more prominent had the Table been carried further. However,
in this Table all things have combined to satisfy the formula with great
accuracy.

In Table HI we come across a fact of an entirely different nature
from the above. Pig. S is the plot of this Table, and gives the values
of at different parts of the rod.

102

Hbnbt a. Bowiaotj

TABLE III.

Bab -89 Inos Diambtdb . 0 at End of Bab .

L .

0 ^

served .

Error of

0 ^

served .

OeSou -

lated .

Error of

19*7

16-8

16-0

16-8

16*6

17*0

17*6

18*4

19 - 2

20 - 8
21-8
22-8
24-8
26-8
28-8
81-8

16-2

16-8

15 - 5

16 - 9 ,
16-8

16 - 9

17 - 6

18 - 4

19 - 4

20 - 5

21 - 7
28-1
24-7
26-5
28-4
80-6

— 4*6
- 1-0
— -6
+ -1
— -2
— -1

+ -2
+ -2
— -1
+ -8
— -1
— -8
— -4
- 1-8

0 -

19-7

36-0

62-0

67-8

84-8

101-8

118-9

137-8

166.5

176-8

198-6

221-4

246-2

278-0

301-8

888-6

16*2

80-6

46-0

61-8

78-1

06-0

112-6

180-9

150*8

170-7

192-2

216-8

289-9

266-4

294-6

825-1

— 4-6
- 5-6
— 6-0
- 6-0
— 6-2
- 6-8
- 6-3
— 6*4
— 6-2
— 6-1
— 6-4
- 6-1
- 6-8
— 6-6
- 7-2
- 8-6

CJ =7.6(10»"i+10-««»i); C'=89a0o«i_.l0-oi7i).

The homontal line in the figure represents values of L, and the verti-
cal ordinates are values of Q'^ The full line gives the observed dis-
tribution, and the dotted line that according to the formula.

The formula gives the distribution very nearly for all points except
those near the end. The formula indicates that Q' decreases contin-
\ially toward the end; but by experiment we see that it increases near
this point. On first seeing this, I thought that it was due to some
residual magnetism in the bar; but after repeating the experiment
several times with proper care, I soon found that this was always the
case. I give the following explanation of it: — ^In the formulse wo have
assumed J2', the resistance of the medium, to be a constant; now this
resistance includes that of the lines of force as they pass from the rod
through the medium and thus back to the other end of the rod; and of

Studies oit Magnetic Distbibution

103

this whole quantity the part which affects the rdative distrihutiou at
any part of the rod most is that of the medium immediately surrounding
that part; and so the parts near the end have the adyantago oyer those
further back, inasmuch as the lines can pass forward as well as outward
into the medium. The same thing takes place in the case of the dis-
tribution of electricity, where the " density ” is inyersely proportional
to the resistance which the lines of inductiye force experience from
the medium; and here we find that the “ density ” is greatest on the
projections of the body, showing that the resistance to the lines of in-
duction is less in such situations, and by analogy showing that this
must also be the case for lines of magnetic force. But this effect is
not yery great in cylinders until quite near the end; for Oonlomb, in a
long electrified cylinder, has found the density at one diameter back
from the end only 1-25 times that at the centre; and so there is prob-
ably a long distance in the centre where the density is sensibly constant.
Hence we may suppose that our second hypothesis, that B' is a con-
stant, will be approximately correct for all parts of a bar except the
ends, though of course this will yary to some extent with the distribu-
tion of the lines in the medium; at least the change in B' will be
gradual except near the end, and so may be partially allowed for by
giying a mean yalue to r.

Hence we see that could the formula be so changed as to include
both the yariation of B and of B', it would probably agree with the
three Tables giyen.

To study the effect of yariation in the permeability more carefully,
we can proceed in another manner, and use the formulae only to get
the yalue of r at different parts of the rods.

Ho matter how r may yary, equations (2) and (3) will apply to a yery
small distance I along the rod; and as the orgin of coordinates may be
at any point on the rod, if Q' and Q' are taken at one point and Q and
Q, at another point whose distance from the first is Z, we shall haye the
four equations

Q^O, +

Q, = orl, Qi = rl 3 ^^ + *-'*).

Calling ^ = H and = Q, we shall find, on eliminating 0 and A
and deycloping s" and e-",

104

Hbnbt a. Bowland

3 (GH+1

or, to a greater degree of approximatioii,

•"=f(Vis(a|i^^ + i)-6) (8J)

Before applying these fonnnlse to any series of observations, the
latter should be freed from most of the irregularities due to accidental
causes. For this purpose the following Tables have been plotted and a
regular curve drawn to represent as nearly as possible the observations;
in other cases a column of differences was formed and plotted. In
either case the ordinates of the curves were accepted as the true quan-
tities. But, for fear that some might accuse me of tampering with my
observations, I have in all cases added these as they were obtained.

TABLE IV.

Bab -19 Inch Diahbtbb. 0 at Obntbb or Bar.

The correction is necessary, because small irregularities in the obser-
vations will produce immense changes in r®.

Table IV contains some of the best observations I have obtained.
It is from a bar 57 inches long with a helix 1-J inch long in the centre
to magnetize it. Each quantity is the mean of six observations, these
beiag made on both ends of the bar and with the current in opposite
directions.

In this Table a source of error was guarded against which I have not

SitroiBS ON Magnetic Distbibution

105

seen ineatioiied elsewhere. When a har of iron is magnetized at any
part and the distrihntion over the rest quickly measured, on being then
allowed to stand some time and the distribution again taken, it will have
changed somewhat, the magnetism having, as it were, crept down the
bar further. Hence in this Table time was allowed for the bar to reach
its permanent state.

On looking over colunm 6, which contains the values of ~=^= Itfa/i

(equation 7), we observe that as Q' decreases, the value of JR'aju first
increases and then decreases. Now it is not probable that B' undergoes
any sudden change of this sort; and so it is probably due to change in
the permeability of the rod. Hence by this method we arrive at the
same results as by a more direct and exact method.’ But by this Tnaamg
we are able to prove in the most unequivocal manner that magnefio
permedbUity is a fimdion of the magnetisation of the iron and net of the
magnetizing force. Hence it is that I have preferred, in my papers on
Magnetic Permeability, to consider it in this way in the formula and
also in the plots, while Dr. Stoletow (in his paper, Phil. Mag., January,
1873) plots the magnetizing-function as a function of the magnetizing
force.

When we plot the results in this Table with reference to Q' and B'afi,
the effect of the variation of M' is apparent; and we see, on comparing
the curve with those given in my paper above referred to, that B' in-
creases as L increases, at least between L—Z and D — 8, which is as
we should suppose from the arrangement of the apparatus. Por this
Table I happen to have data for determining Q in absolute measure;
and these show that the maximum value of fx should be about where
the Table shows it to be.

This method of finding the variation of ft is analogous to that of
finding conductivity for heat by raising the temperature of one end
of a bar and noting the distribution of heat over the bar; indeed the
curves of distribution are nearly the same in the two oases.

If it were thought worth while, it would be very easy to obtain a
curve of magnetic distribution for a rod and then enclose the whole
rod m a helix and determine its curve of permeability. This would
give data for determining B' in absolute measure at every point of the
rod.

To complete the argument that the variation of r* is in great measure
due to that of ft, I have caused the magnetizing force on a bar to vary.

Tphil. Mag., Aug-ust, 1878.

106

Hbnet a. Rowland •

Tables V, VI, and VII are from a bar 9 feet long and *25 inch in
diameter. At the centre a single layer of fine wire was wound for a
distance of 1 foot; and the current for magnetizing the bar was sent
through this. The zero-point was at the centre of this helix and at the
centre of the bar; so that the observations on the first 6 inches include
the part of the bar covered by the helix.

The values of are the sum of four observations on each end of
the bar and with the current reversed. The three Tables are compar-
able with each other, the same arbitrary unit beiug used for all.

TABLE V.

Maonbtizin© Cubebbt - 176 .

Here we see an excellent confirmation of the results deduced from
Table lY. In Table V, where the magnetizing force is very small, and
where, consequently, no part of the iron has yet reached its TniuiTnuTn

resistance, the value of — , = ^ = Rap. decreases continually as the value

of Q' decreases, as it should do. In Table VI, with a higher magnetiz-
iug power, which was sufiBcient to bring a portion of the bar to about

the minimuTn resistance, we see that ^ remains nearly stationary for a

short distance from the helix and then decreases in value. In Table
Vn, where the bar is highly magnetized and the portion near the zero-

Sttjdibs on Magnbtio Distbibxttion

lOY

TABLE VI.

Magkbtizxng^ Curbbkt <81.

li.

servod.

Qi-

Coiv

rooted.

Cor-

rected.

rs.

o^k-

lated.

9 i

10 i

12 (

18 1

14 (
16}

16 (

17 1
18)
End.

16*8

32*0

83*4

48*8

66*9

55*2

46*8

81*8

61*8

46*4

86*4

22*0

48*0

56«i

48*1

43*8

87*4

88 0
39*0
25*8
31*9
18*7
16*6
13*7
9*8

891*9
886*8
388-7
346*4
309 0
176-0
147*0
131*7
99*8
81*1
65*5
52*8

*0204

*0301

•0302

*0230

*0248

*0262

•0800

*0852

*0405

•0479

49*0

49-7

49*5

45*5

41*2

88*2

88*8

28-4

24*7

20*9

17*8

22*8

83*38

48*84

56*90

m ^

TABLE VII.

IlfAOVfBTXZIKO CUBRBBT 1*1!^.

8
9

13
18

14
16
16
17

15
19
30

End.

OOB-

Oor-

r*.

rSy-

Oalou-

served.

rooted.

reoted.

r«

lated.

8*5

9*4

15*4

37*5

44*8

66*6

71*2

762*4

758-9

749*5

784*1

706*6

662*8

695*7

534*6

464*8

418*6

868*4

838*1

291*8

257*8

237*8

199*8

178-9

151*3

180*3

112*8

96*8

•V2V9

41:3

3*58

8*39

15*78

26*70

48*86

69*87

59*6

B9-7

•0300

50*0

51*0

51*2

*0162

61*7

45-3

46*2

*0141

70*9

40*8

*0130

88*8

86*8

*0107

98*5

88*8

88*5

*0110

90*9

80*6

80*5

*0116

86-3

28-1

38*0

*0118

84*7

25*6

35*4

•0140

71*4

38*4

22*7

*0147

68*0

20*0

30-8

*0161

63*1

84*0

96*8

18*1

16*0

•0180

65*6

108

Henbt a. Rowland

points approaches the maximum of magnetization, increafles in value

as "we pass down the har; and having reached its maximnin at Z/= Ilf
nearly, it decreases. These Tables, then, show in the most striking
manner the effect of the variation of the magnetic permeability of iron
upon the distribution of magnetism.

It is evident that these Tables also give the data for obtaining the
relative values of jB' at different parts of the bar; hut the results thus
obtained are conflicting, and will need further experiment to obtain
accurate results. Where such a small magnetizing force is used as in
Table V it is almost impossible to attain accuracy; and allowance should
he made for this in deducing results from it. The greatest liability to
error is of course where the magnetization is small; for any small re-
sidual magnetism which the bar may contain will be more apparent
here — although great care was taken to remove all residual magnetism
before use. Besides this there are many other disturbances from which
the higher magnetizing powers are free.

If we accept Greenes formula as correct, observations give us data
for determining the magnetizing-f unction of iron in a unique manner^ for
nearly all other methods depend on absolute measurements of some
kind. Thus the least value of r® in Table IV for a rod '19 inch diam-
eter is -0142, which gives p = •01132, which in Greenes formula (equa-
tion 8) gives = 3388 for the greatest permeability of this iron; and
this is as nearly right as we can judge for this kind of iron. It is to be
noted that Greenes formula has been found for the portion of the bar
covered by the helix; but, as seen from my formula, it will approxi-
mately apply to all portions, though it would be better to find a new
formula for each case.

We shall, toward the last, resume this subject again; and so will leave
it for the present.

The results which I have now given, and indeed all the results of this
paper, have been deduced not only from the observations which I pub-
lish, but from very many others; so that my Tables may be considered
to represent the average of a very extended series of researches, though
they are not really so.

Let us now consider the case of that portion of the bar which is
covered by the helix. First of all, when the helix is symmetrically
placed on the rod, equations (5) and (6) will apply. As (J" is the

Studies on Mao-netio Disteibution

109

quantity which is usually taken to represent the distribution of mag-
netism, being nearly proportional to the ^^surface-density” of mag-
netism, I shall principally discuss it.

In the first place, then, this equation (5) shows that the distribution
of magnetism in a very elongated electromagnet, and indeed in a steel
magnet, does not change when pieces of soft iron bars of the same
diameter as the magnet are placed against the poles, provided that eqml
pieces are applied to both ends; otherwise there is a change. This result
would be modified by taking into account the variation of the permea-
bility, &c.

Let us first consider the case where the rod projects out of the end
of the helix, as in Tables V, YI, and Vli. By giving proper values to
the constants, we obtain the results given in the last column of the

TABLE VIII.

Strenjrth of magrnetlzlngr current.

*108.

•m.

•878.

•600.

t 2-7

f 2-4

8-8

4*0

6-7

8-2

2*7

8-9

6-0

8-7

•7

•9

-9

1-7

4-0

9-8

•6

•8

-8

8*2

14-7

Tables. The agreement with observation is in most cases very perfect.
We also see the same variation of r that we before noticed in the rest of
the curves, and we see that it is in just the direction theory would
indicate from the change of /i.

In these Tables we come to a very important subject, and one to
which I called attention some years back — ^namely, the change in the
distribution when the magnetizing force mries^ and which is due to change
of permeability. The following Tables and figures show this extremely
well, and are from very long rods with a helix a foot long at their
centre, as in the last three Tables. The bar in both these Tables was
•19 inch in diameter and 5 foot long. The zero-point was at the centre
of the bar and of the helix. The Tables give values of for the
magnetizing forces which appear at the bead of each column, and which
are the tangents of the angles of deflection of the needles of a tangent-
galvanometer. Table VIII only gives the part covered by the helix.
Both Tables are from the mean of both ends of the bar.

110

Hbnet a. Rowland

These experiments show in the most positive manner the effect we
are considering; and we are impressed by them with the great compli-
cation introduced into magnetic distribution by the variable character
of magnetic permeability.

In Kg. 3 I have represented the distribution on half the bar, as given
in Table IX, the other half being of course similar. Here the greatest

TABLE XX.

Fig. 3.— Plot of Table IX, showing surface-density for different values of the

magnetizing force.

change is observed in the part covered by the helix, though there is
also a great change in the other part. These Tables show that, as
the magnetization of the bars increases, at least leyond a certain point,
the curves on the part covered by the helix increase in steepness; and
the figure even shows that near the middle of the helix an increase of
magnetizing force may cause the surface-density to decrease; and Table
Vm shows this even better. Should we calculate Q", however, we
should always find it to increase with the magnetizing force in all cases.
These effects can be shown also in the case where the bar does not

SlITDlBS ON Mi-GNEaiO DlBTBIBXTTION

111

extend beyond the helix, but not nearly so 'vrell as in this case, seeing
that here Q" can obtain a greater value.

Asstmung that fx is variable, the formula indicates the same change
that we observe; for as Q" increases from zero upwards, [x will first
increase and then decrease; so that as we increase the magnetizing force
from zero upwards, the curve should first decrease in steepness and
then increase indefinitely in steepness. In these Tables the decrease
of steepness is not very apparent, because the magnetization is always
too great; and indeed on this account it is difficult to show it; but in
Tables V, "VI, and VII this action is shown to some extent by the

TABLS X

(cbdA L.

-245.

*860.

•600.

1-00.

+ 17-6

+ 29-4

452-0

4108-7

+ 9-6

+ 16-8

+ 81-6

4 60-1

4 7-4

418-1

424-8

4 46-8

+ 6-4

4 9-8

419-1

4 84-1

4 8-4

+ 7*2

414-7

4 22-8

+ 2-0

4 4-6

4 9-9

4 16-0

4 0-6

4 2-4

4 5-4

4 9-6

— 0-8

4 0-8

4 1-2

4 0-6

— 1*8

— 1-6

— 2-1

— 0-8

— 80

— 8-6

— 6-6

— 8-8

— 5-0

— 6-8

— 8-6

— 15-6

— 7-4

-10-0

—16-4

— 27-1

— 8-4

-10-0

—16-9

— 26-5

— 60

— 7-9

—14-6

— 22-6

— 6-2

— 7-0

-12-6

— 21-0

....

— 5-8

—11-9

— 19-0

....

— 9-4

-19-1

— 81-2

....

— 5-8

—16-2

....

-- 6-5

— 5-6

— 0-7

—19-8
— 6-0
— 1-2

values of r in the formula. The change of distribution with the helix
arranged in this way at the centre of the bar is greater than in almost
every other case, because the magnetism of the bar, Q", can change
greatly throughout the whole length of the helix, and thus the value
of r be changed, and so the distribution become different.

The next case of distribution which I shall consider is that of a very
long rod having a helix wound closely round it for some distance at
one end.

Table X is from a bar 9 feet long with a helix wound for one foot
along one end. The bar was -86 inch in diameter. All except the first

112

Heney a. Eowland

column is tte sum of two results with the current in opposite direc-
tions, and after letting the bar stand for some time, as indeed was done
in nearly every ease. The first column contains twice the quantities
observed, so as to compare with the others. The zero-point was at the
end of the bar covered by the helix.

The value of between 0 and 1 includes the lines of force passing
out at the end of the bar, and is therefore too large.

In Fig. 4 we have a plot of the results found for this bar. The
curves are such as we should expect from our theory, except for the
variations introduced by the causes which we have hitherto considered.
Thus the sharp rise in the curve when near the end of the bar has
already been explained in connection with Table III. A small portion

of it, however, is due to those lines of induction which pass out through
the end section of the bar; and in future experiments these should be
estimated and allowed for.*

To estimate the shape of the curve theoretically in this case, let us
take equation (4) once more, and m it make s'=oo and s"= ^
which will make it apply to this case. We shall then have A' = — 1,
and A" = 00 , whence for the positive part of we have

~ ^ ^

and for the negative part

**Whoii couBldorinf^ surfaco-density, we shotild also allow for the direct action of
the helix, thoiijj^h this is always found too small to be worth taking into account
except in verj* accurate experiments.

Studies on Magnetic Distbibution

113

therefore the real value is

q: =

/gr{r—b)/g—ri

Witr ^ ^

- 2 ) +

E‘

')•

And if « is reckoned from the end of the rod, "we have

When !C=0, ttds becomes

^4L

%li!r

e-*(2 — ae-*);

. . (10)

and when a; = 6, it becomes

the ratio of which is

J (e-^ - 1) ;

and this is the ratio of the values of Q" at the ends of the helix.
When 5 is 12 inches, as in this case, we get the following values of this
ratio: —

•OT).

•1.

•15.

•20.

•80.

00.

•8404

•4178

•4546

•4863

—S3

4-48

2-86

2-40

2-20

2-00

2*00

To compare this with our experiments, let us plot Table X once more,
rejecting, however, the end observations and completing the curve by
the eye, thus getting rid of the error introduced at this point. We then
find for this ratio, according to the different curves,

B. 0. D.

2*1 2-3 3-2

It is seen that these are all above the limit 2, as they should be —
though it is possible that it may fall below in some cases, owing to the
variation Qf the permeability. As the magnetization increases, the
values of the above ratio show that r decreases, as we should expect it
to do from the variation of ii-.

To find the neutral point in this case, we must have in fotmula (10)

= 2s’'* — 1 ,

114

HEliTEY A. EOWIiAND

where x is the distance of the neutral point from the end. Making
b = 12, we have from this : —

•05.

*10.

•B.

•SO.

•80.

oo.

a!=

10-1

8*90

8-81

7-80

7-8!)

«-00

By experiment we find that the neutral point is, in all the cases we
have given in Table X, between 7* *6 and 8*1 inches, which are quite
near the points indicated by theory for the proper values of r, though
we might expect curve D to pass through the point » = 9, except for
the disturbing causes we have all along considered.

Our formulae, then, express the general facts of the distribution in
this case with considerable accuracy.

These experiments, and calculations show the change in distribution
in an electromagnet when we place a piece of iron against one pole only.
In an ordinary straight electromagnet the neutral point is at the
centre. When a paramagnetic substance is placed against or near one
end, the neutral point moves toward it; but if the substance is diamag-
netic it moves from it.

The same thing will happen, though in a less degree, in the case of a
steel magnet; so that its neutral point depends on external conditions
as well as on internal.

We now come to practically the most interesting case of distribution,
namely that of a straight bar magnetized longitudinally either by a
helix around it, or by placing it in a magnetic field parallel to the lines
of force; we shall also see that this is the case of a steel magnet mag-
netized permanently. This case is the one considered by Biot {TraiU
de Phys,, tome iii, p. T"?) and Green (Mathematical Papers of the late
George Green, p. Ill, or Maxwell's ^ Treatise,' art. 439), though they
apply their formulae more particularly to the case of steel magnets.
Biot obtained his formula from the analogy of the magnet to a Zamboni
pile or a tourmaline electrified by heat. Green obtained his for the
case of a very long rod placed in a magnetic field parallel to the lines
of force, and, in obtaining it, used a series of mathematical approxima-
tions whose physical meaning it is almost impossible to follow. Prof.
Maxwell has criticised his method in the following terms (^Treatise,'
art. 439): — "Though some of the steps of this investigation arc not
rigorous, it is probable that the result represents roughly the actual
magnetization in this most important case." Prom the theory which

Studies on Maqnbtio Disteibuiion

116

T have given in the first part of this paper we can deduce the physical
meaning of Green’s approximations; and these are included in the
hypotheses there given, seeing that, when my formula is applied to the
special case considered hy Green, it agrees with it where the permea-
bility of the material is great. My formula, however, is far more gen-
eral than Green’s.

It is to Green that we owe the 'important remark that the distribu-
tion in a steel magnet may he nearly represented hy the same formula
that applies to electromagnets.

As Green uses what is known as the surface-density of magnetization,
let us first see how this quantity compares with those I have used.

Suppose that a long thin steel wire is so magnetized in the direction
of its length that when broken up the pieces will have the same mag-
netic moment. While the rod is together, if we calculate its effect on
exterior bodies, we shall see that the ends are the only portions which
seem to act. Hence we may mathematically consider the whole action
of the rod to he duo to the distribution of an imaginary magnetic fiuid
over the ends of the rod. As any case of magnetism can he represented
by a proper combination of these rode, we see that all cases of this sort
can he calculated on the supposition of there being two magnetic fiuids
distributed over the surfaces of the bodies, a unit quantity of which
will repel another unit of like nature at a unit’s distance with a unit of
force. The surface-density at any point will then be the quantity of
this fiuid on a unit surface at the given point; and the linear density
along a rod will he the quantity along a unit of length, supposing the
density the same as at the given point.

Where we use induced currents to measure magnetism we measure
the number of lines of force, or rather induction, out hy the wire, and
the natural unit used is the number of lines of a unit field which will
pass through a unit surface placed perpendicular to the lines of force.
The unit pole produces a unit field at a unit’s distance; hence the num-
ber of lines of force coming from the unit pole is 47r, and the linear
density is

) Qs

and the surface-density

( 11 )

( 12 )

These really apply only to steel magnets; but as in the case of electro-
magnets the action of the helix is very small compared with that of the

116

TTukt -rt a. Eowlanb

iron, especiaUy when it is very long and the iron soft,’ we can apply
these to the cases we consider.

Transforming Q-reen^s formula into my notation, it gives

gr (6 -IB) _ gfX

. . (13)

in. which k is E’enmann’s coefficient of magnetization by induction, and

is equal to

47r

14 ^“

(U)

This equation then gives

<2;'=

Equation (5) can be approximately adapted to this case by making
a' = 00 , which is equivalent to neglecting those lines of force which
out of the end section of the bar. This gives A'——l; hence

(IS)

0"-

Eow we have found (equation 7) that r = ^ ^ nearly; and

this in Green’s formula (equation 14) gives

0"-AL ^ .... (16)

which is identical with my own when fi is large, as it always is in the
ease of iron, nickel, or cobalt at ordinary temperatures.

When X is measured from the centre of the bar, my equation, becomes

X =

- _5.

47r V JiJ?

rb _»’6

( 17 )

The constant part of Biot’s formula is not the same as this; but for any
given case it will give the same distrihution. ^

Both Biot and Green have compared their formulae with Coulomb’s
experiments, and found them to represent the distribution quite well.
Hence it will not be necessary to consider the case of steel magnets very
extensively, though I will give a few results for these further on.

»! take this occasion to correct an error in Jenkin’s ‘Textbook of Electricity,’
where it is stated that hy the introduction of the iron bar into the hoUx, the num-
ber of lines of force is increased 32 times. The number should have boon from a
quite small number for a short thick bar and hard Iron to nearly 0000 for a lonj?
thin har and softest iron.

Studies on Magnetic Distribution

117

At present let ns take the case of electromagnets.

Por observing the effect of the permeability, I took two wires 1^-8
inches long and -19 inch in diameter, one being of ordinary iron and
the other of Stubs^ steel of the same temper as when purchased. These
were wound uniformly from end to end with one layer of quite fine
wire, making 600 turns in that distance.

In finding A from Q'', the latter was divided by 47r JL, except at the
end, where the end-s%3tion was included with JL in the proper manner.
X was measured from the end of the bar in inches.

The observations in Table XI are the mean of four observations
made on both ends of the bar and with the current in both directions.

TABLE XI.

Iron Elbotbomagrbt.

X ^ distance
from end.

Q«-

Observed.

4irX.

Observed.

4irA,

Computed.

Error.

22-5

41-1

88*9

—7-2

12*6

26*1

26-9

+ 1-8

19-8

19*8

18-9

— 0-4

12-0

11-7

— -8

6-6

7-1

+ -6

8-9

4-0

+ -1

2-9

1.7

— 1-2

47r^ = 42

The agreement with the formula in this Table is quite good; but we
still observe the excess of observation over the formula at the end, as
we have done all along. Here, for the first time, we see the error
introduced by the method of experiment which I have before referred
to (p. 98) in the apparently small value of at a; = -76.

On trying the steel bar, I came across a curious fact, which, how-
ever, I have since found has been noticed by others. It is, that when
an iron or steel bar has been magnetized for a long time in one direction
and is then demagnetized, it is easier to magnetize it again in the same
direction than in the opposite direction. The rod which I used in this
experiment had been used as a permanent magnet for about a month,
but was demagnetized before use. Prom this rod five cases of distribu-
tion were observed first, when the bar was used as an electromagnet
with the magnetization in the same direction as the original mag-

118

Henet a. EowiiAITd

netism; second, ditto with magnetization contrary to original mag-
netism; third, when used as a permanent magnet with magnetism the
same as the original magnetism; fourth, ditto with magnetism oppo-
site; and fifth, same as third, but curve taken after several days. The
permanent magnetism was given by the current.

The observations in Tables XI and XII can be compared together,
the quantities being expressed in the same unknown arbitrary unit.
It is to be noted that the bars in Tables XI and XII were subjected to
the same magnetizing force.

TABLE XII.
Stubs* Stbbl.

Eleotromagnet.

Permanent Magnet.

Magnetism
same as
orlglnaL

Magnetism
opp site to
original.

Magnetism
same as
original.

MagnStlsm
opposite to
original.

Same as third,
after three or
four days.

Q.-

4irX.

Q.-

4irX.

Q.-

4ir\.

Q«-

4irX.

28-8

11-6

8*2

6*1

7*4

8*6

1-7

42-5

28*0

16*4

12*2

7-4

8*6

•8

16*9

7-7

6-9

4-8

6-6

2-7

1*0

29*0

16-4

11*8

8-6

6-6

2-6

•5

^14*4

j. 8-2

^ 6-8
8*0
2*2

18-7

8*2

5*8

8-0

1*1

4-8

4*0

2*9

1*6

•9

4-6

4-0

2*9

1-6

12*8

7*8

4*8

2*9

2*0

12*2

7*8

4*8
2*9
1*0 •

First of all, from these Tables and figures (p. 119) we notice the
change in distribution due to the quality of the substance; thus in Fig. 5
we see that the curves for steel are much more steep than that of iron,
and would thus give greater values to r in the formula — a result to be
expected. We also observe in both figures the great change in distri-
bution due to the direction of magnetization. In the case of the elec-
tromagnet this amounts to little more than a change in scale; but in
the permanent magnet there is a real change of form in the curve. It
seems probable that this change of form would be done away with by
using a sufficient magnetiziug power or magnetizing by application of
permanent magnets; for it is probable that the fall in the curve E is
due to the magnetizing force having been sufficient to change the
polarity completely at the centre, but only partially at the ends.

On comparing the distribution on electromagnets with that on perma-
nent magnets, we perceive that the curve is steeper toward the end in

Stttdies on Magnbtio Disteibtjtion

119

electromagnets than in permanent magnets. At first I thought it
might he due to the direct action of the helix, but on trial found that
the latter -was almost inappreciable. I do not at present kno-w the
explanation of it.

As before mentioned. Coulomb has made many experiments on the
distribution of magnetism on permanent magnets ; and so I shall only
consider this subject briefly. I hare already given one or two results
in Table XII.

Fia. 5. — Results from olectromsguots.

A. Iron, from Table XI.

B. Steel, from Table XII, magnetized same as originally.

0. Steel, from Table Xll, magnetized opposite to its original magnetism.

ITxa. 0. — Results from steel permanent magnets.

D. MCagnetized in its original direction, Table XII.

E. Magnetized opposite to its original direction, Table XII.

Scale four times that of Fig. 6.

The following Tables were taken from two exactly similar Stnbs^
stool rods not hardened, one of which was subsequently used in the
experiments of Table XII. They were 12-8 inches long and '19 inch
in diameter.

The coincidence of these observations with the formula is very re-

120

Hbnby a. Eowlastd

markaWe; but still we see a little tendency in the end obseivation to
rise above the value given by the formula.

In equation (7), and also from Green’s formula, we have seen that

for a given quality and temper of steel p = -^ is a constant. Prom

CoulomVs experiments on a steel bar *176 inch in diameter (whose
quality and temper is uiiknown, though it was probably hardened) Green
has calculated the value of this constant, and obtained *05482, which
was found from the French inch as the unit of length, but which is
constant for all systems. From Tables XIII and XIV we find the value

TABLE XIIT.

Q«-

Observed.

4n-X.

Observed.

4irA.

Computed.

Error.

1-28

2-56

8*84

5- 12

6- 40

46>6

28*8

12-6

7-2

2-8

84-9

18-6

9*8

5-6

1*8

84 >26
18-60
9-88
4-77
1-41

-•6

+ •1
— 8
— 4

4nrX= -10'®'*').

TABLE XIV.

Q«-

Observed.

4irX.

Observed.

4irA.

Computed.

Error.

1-28

2-66

8-84

6-12

6-40

42>6

81-9

80-74

— 1

•2

31-4

16-7

16-72

10-9

8-5

8-86

-4

6-4

4-2

4-28

•1

1-7

1-88

1-27

•1

4irX=-105(10'®"<*—

-10’*®®*).

of r to be -4674, whence = -04440 for steel not hardened. As the

steel becomes harder this quantity increases, and can probably reach
about twice this for very hard steel.

To show the effect of hardening.. I broke the bar used in Table XIV
at the centre, thus producing two bars 6*4 inclies long. One of these
halves was hardened till it could scarcely be scratched by a file; but the
other half was left unaltered. The following Table gives the distribu-
tion, using the same unit as that of Tables XIII and XIV. The bars
were so short that the results can hardly be relied on; but they will at
least suffice to show the change.

Studies on Magnetic Disteibution

121

In Pig. ^ I have attempted to give the curve of distribution from
Table XV, and have made the curves coincide with observation as nearly
as possible, making a small allovrance, however, for the errors intro-
duced by the shortness of the bar. It is seen that the effect of harden-
ing in a tar of these dimensions is to increase the quantity of magnetism,
but especially that near the end. Had the lar leen very long, no increase

TABLE XV.

Soft Steel, A.

Hard Steel, B.

Q.-

4irX.

Qe*

4irA.

•64:

1-28

1-92

8-20

20-4

29-1

47-7

68-1

0-8

16-8

18*9

21-7

6-0

9-4

7-0

11-0

8-8

8-0

2-6

2-0

Fig. 7. — UoBultB from permanent magnets.

A. Soft steel.

B. Hard steel.

in the total quantity of magnetism would have tahen place; lut the distri^
iution would have leen changed. Prom this we deduce the important
fact that hardening is most useful for short magnets. And it would seem
that almost the only use in hardening magnets at all is to concentrate the
magnetism and to reduce the weight. Indeed I have made magnets from
iron wire whose magnetization at the central section was just as intense
as in a steel wire of the same size; but to all appearance it was less

122

Kbnbt a. Eowlajjd

strongly magnetized than the steel, becanse the magnetism was more
diffused; and as the magnetism was not distributed so nearly at the end
as in the steel, its magnotis moment and time of vibration were less.

It is for these reasons that many makers of surveyors’ compasses find
it unnecessary to harden the needles, seeing these are long and thin.

We might deduce all these facts from the formulss on the assumption
that r is greater the harder the iron or steel.

Having now considered briefly the distribution on electromagnets
and steel magnets, and found that the formulae represent it in a general
way, we may now use them for solving a few questions that we desire
to solve, though only in an approximate manner.

YI.

M. Jamin, in hie recent experiments on magnetic distribution, has
obtained some very interesting results, although I have shown his
method to be very defective. In his experiments on iron bars mag-
netized at one end, he finds the formula r* to apply to long ones as I
have done. How it might be argued that as the two methods apparmily
give the same result, they must be equally correct. But let us assume
that the attraction of his piece of soft iron F varied as some unknown
power n of the surface-density 3. Then we find

F=Ce’^^

which shows that the attractive force or any power of that force can
be represented by a logarithmic curve, though not by the same one.

the error introduced by M. Jamin’s method is insidious and not
easily detected, though it is none the less hurtful and misleading, but
rather the more so.

However, hie results with respect to what he calls the normal mag-
net” are to some extent independent of these errors; and we may now
consider them.

Thus, in explaining the effect of placing hardened steel plates on
one another, he says, "Quand on superpose deux lames aimant^es
pareilles, les courbes qui repr6sontent les valeurs de F [the attractive
force on the piece of soft iron] s’616vent, parce que le magn6tisme quitte
les faces que Ton met en contact pour se rSfugier sur les parties ex-
t4rieures. En m6me temps, les deux courbes se rapprochent Tune d(^
I’autre et du milieu de raimant. Get effet augmente avec une troisiSmo

lotOn the Theory of the Normal Magnets,’ Comptes Bmdus^ March 31, 1878;
translated In Phil. Mag., June, 1878.

Studies oet Magnetic Distkibution

1^3

lame et avee une quatri&me. Finalement les deux courbes se joignent
au milieu/^

In applying tbe formula to this case of a compound magnet, we have
only to remark that when the bars lie closely together they are theoret-
ically the same as a solid magnet of the same section, but are practically
found to be stronger, because thmbars can be tempered more uniformly
hard than thick ones. The addition of the bars to each other is similar,
then, to an increase in the area of the rod, and should produce nearly
the same effect on a rod of rectangular section as the increase of

diameter in a rod of circula.r section. No'w the quantity is

nearly constant in these rods for the same quality of steel, whence r
decreases as d increases^ and this in equation (I'?) shows that as ihe
diameter is increased, the length being constant, the curres become
less and less steep, until they finally become straight lines. This is
exactly the meaning of M. Jamin’s remark.

Where the ratio of the diameter to the. length is small, the curres of
distribution are apparently separated from each other and are given by

the equation

k =

47tVi2i?

. (18)

which is not dependent on the length of the rod. This is exactly the
result found by Coulomb (Biot’s Physique, vol. iii, pp. U, 76). M.
Jamin has also remarked this. He states that as he increases the num-
ber of plates the curves approach each other and finally unite; this he
caUe the “normal magnet;” and he supposes it to be the magnet of
greatest power in proportion to its weight. “From this moment,”
says he, “the combination is at its maximum.” The normal magnet,
as thus defined, is very indefinite, as M. Jamin himself admits.

By our equations we can find the condition for a maximum, and can
give the greatest values to the following, supposing the weight of the
bar to be a fixed quantity in the first three.

Ist. The magnetic moment.

8nd. The attractive force at the end.

3rd. The total number of lines of magnetic force passing from the
bar.

4th. The magnetic moment, the length being constant and diameter
variable.

Either of these may be regarded as a measure of the power of the
bar, aecording to the view we take. The magnetic moment of a bar is
easily found to be

124

Hbnbt a. EcywiiAND

and if 7 ' is the weight of a unit of Toliome of the steel and W is the
weight of the magnet, we have finally

u- « -P ^

- 4s:^0'n 2~

E® -1 \
+ 1^’

• (ao)

where =

This only attains a maadmmn when gz=oo, or the rod is infinitely

long compared with its diameter.

The second case is rather indefinite, seeing it will depend upon
whether the hody attracted is large or small. When it is small, we
reqnire to make the surface-density a maximum, the weight being con-
stant. We find

a.=

-t-i

( 21 )

which attains a maximum as before when °o ■

When the attracted

body is large, the attraction will depend more nearly upon the linear
density,

( 22 )

which is a maximum when

For the third case we have the value of Q" at the centre of the bar
from equation (6),

® (a»’‘-l)»

(23)

The condition for a maximum gives in this case

&_l-65

d~ p ’

For the last case, in which the magnetic moment for a given length
is to be made a maximxim, we find

5_-l

d—p

This last result is useful in preparing magnets for determining the

Studies ok Magketio Distributiok

125

intensity of the earth’s magnetism, and shows that the magnets should
he made short, thick, and hard for the best efEect."

But for all ordinary purposes the results for the second and third
cases seem, most important, and lead to nearly the same result; taking
the mean we find for the maximum magnet

(24)

d-p

We see from all our results that the ratio of the length of a magnet
to its diameter in aU cases is inversely as the constant p. This con-
stant increases with the hardness of the steel; and hence the harder the
steel the shorter we can make our magnets. It would seem from this
that the temper of a steel magnet should not be drawn at all, hut the
hardest steel used, or at least that in which p was greatest. The only
disadvantage in using very hard steel seems to be the difficulty in
imparting the magnetism at first; and this may have led to the practice
of drawing the temper; hut now, when we have such powerful electro-
magnets, it seems as if magnets might he made shorter, thicker, and
t.TniTi is the custom. With the relative dimensions of magnets
now used, however, hardening might be of little value.

We can also see from all these facts, that if we make a compoimd
magnet of hardened steel plates there will be an advantage in filing
more of them together, thus making a thicker magnet than when they
are softer. We also observe that as we pile them up the distribution
changes in just the way indicated by M. Jamin, the curve becoming
less an«fTess steep.

Substituting in the formula the value of p which we have found for
Stub’s steel not hardened, but still so hard as to rapidly dull a file, we
find the best ratio of length to diameter to .be 33-8 — and for the same
steel hardened, about 17, though this last is only a rough approxima-
tion. This gives what M. Jamin has (jp.lled the normal magnet. The
ratio should be lees for a U-magnet than for a straight one.

For all magnets of the same kiud of steel in which the ratio of
length to diameter is constant the relative distribution is the same;
and this is not only true for our approximate formula, but would be
found so for the exact one.

Thus for the " normal magnet ” the distribution becomes

u Weber rocommenda square bars olqlit times aa long us they are broad, and tem-
pered very hard. (Taylor’s Scientific Memoirs, 70 I. il, p. 86.)

186

Histet a. Eowland

where C is & eonstant, and x is meastured from the centre. The distri-
bution will then he as follows : —

25”

•1.

*2.

•8.

*4.

•6.

4-98

•809

1*27

2-06

8*02

This distribution is not the same as that given by M. Jamin; but as
his method is so defective, and his “ normal magnet ” so indefinite, the
agreement is sufidciently near.

The surface-density at any point of a magnet is.

_ e -»V

. . ( 28 )

•27 h

wHcli, for the same kind of steel, is dependent only on ^ and g-
Hence in two similar magnets the surface-density is the same at similar

points, the linear density is proportional to the linear dimensions, the
surface integral of magnetic induction over half the magnet or across
the section is proportional to the surface dimensions of the magnets,
and the magnetic moments to the voltes of the magnets. The forces
at similar points with regard to the two magnets will then he the same.
All these remarks apply to soft iron under induction, provided the
inducing force is the same — and hence include Sir William Thomson's
well-known law with regard to similar electromagnets; and they are
accurately true notwithstanding the approximate nature of the formula
from which they have here been deduced.

Our theory gives us the means of determining what effect the boring
of a hole through the centre of a magnet would have. In this case R'

Studies on Magnetic Distribution

127

is not much affected, but R is increased. Where the magnet is used
merely to affect a compass-needle, we should then see that the hole
through the centre has little effect where the magnet is short and thick;
but where it is long, the attraction on (he compass-needle is much dimin-
ished. Where the magnet is of the U-form, and is to be used for
sustaining weights, the practice is detrimental, and the sustaining-power
is diminished in the same proportion as the sectional area of the magnet.
The only case that I know of where the hole through the centre is an
advantage, is that of the deflecting magnets for determining the inten-
sity of the earth^s magnetism, which may be thus made lighter without
much diminishing their magnetic moment.

In conclusion, let me express my regret at the imperfection of the
theory given in this paper; for although the equations are more general
than any yet given, yet stHl they rest upon two quite incorrect hypoth-
eses; and so, although we have found these formulte of great use in
pursuing our studies on magnetic distribution, yet much remains to be
done. A nearer approximation to the true distribution could readily
be obtained; but the result would, without doubt, be very complicated,
and would not repay us for the trouble.

In this paper, as well as in all others which I have published on the
subject of magnetism, my object has not only been to bring forth new
results, but also to illustrate Farada/s method of lines of magnetic
force, and to show how readily calculations can be made on this system.
For this reason many points have been developed at greater length than
would otherwise be desirable.

ON THE MAGNETIC EFFECT OF ELBCTEIC CONVECTION’

{,Am&rican Journal of Scimce LS], XF, 80-88, 1878]

The experiments described in this paper were made with a view of
determining whether or not an electrified body in motion produces
magnetic effects. There seems to be no theoretical ground upon which
we can settle the question, seeiug that the magnetic action of a con-
ducted electric current may be ascribed to some mutual action between
the conductor and the current. Hence an experiment is of value. Pro-
fessor Maxwell, in his ^ Treatise on Electricity,' Art. 770, has computed
the magnetic action of a moving electrified surface, but that the action
exists has not yet been proved experimentally or theoretically.

The apparatus employed consisted of a vulcanite disc 21-1 centi-
metres in diameter and -6 centimetre thick which could be made to
revolve around a vertical axis with a velocity of 61* turns per second.
On either side of the disc at a distance of *6 cm. were fixed glass plates
having a diameter of 38*9 cm. and a hole in the centre of 7*8 cm. The
vulcanite disc was gilded on both sides and the glass plates had an
annular ring of gilt on one side, the outside and inside diameters being
24*0 cm. and 8-9 cm. respectively. The gilt sides could be turned
toward or from the revolving disc but were usually turned toward it so
that the problem might be calculated more readily and there should
be no uncertainty as to the electrification. The outside plates were
usually connected with the earth; and the inside disc with an electric
battery, by means of a point which approached within one-third of a
millimetre of the edge and turned toward it. As the edge was broad,
the point would not discharge unless there was a difference of potential
between it and the edge. Between the electric battery and the disc,

1 The experiments described were made in the laboratory of the Berlin University
through the kindness of Professor Helmholtz, to whoso advice they are greatly in-
debted for their completeness. The idea of the experiment ilrst occurred to me in
18G8 and was recorded in a note book of that date.

On the Magnetic Beeeot of Elbotsio Oonteotion 129

a commutator was placed, so that the potential of the latter conld be
made plus or minus at will. All parts of the apparatus were of non-
magnetic material.

Over the surface of the disc was suspended, from a bracket m the
wall, an extremely delicate astatic needle, protected from electric
action and currents of air by a brass tube. The two needles were 1‘6
cm. long and their centres 17-98 cm. distant from each other. The
readings were by a telescope and scale. The opening in the tube for
observing the mirror was protected from electrical action by a metallic
cone, the mirror being at its vertex. So perfectly was this accom-
plished that no effect of electrical action was apparent either on charg-
ing the battery or reversing the electrification of th« disc. The needles
were so far apart that any action of the disc would be many fold greater
on the lower needle than the upper. The direction of the needles was
that of the motion of the disc directly below them, that is, perpendicular
to the radius drawn from the axis to the needle. As the support of
the needle was the wall of the laboratory and the revolving disc was on a
table beneath it, the needle was reasonably free from vibration.

In the jdrst experiments with this apparatus no effect was observed
other than a constant deflection which was reversed with the direction
of the motion. This was flnaUy traced to the magnetism of rotation
of the axis and was afterward greatly reduced by turning down the
axis to -9 cm. diameter. On now rendering the needle more sensitive
and taking several other precautions a distinct effect was observed of
several millimetres on reversing the dectrification and it was separated
from the effect of magnetism of rotation by keeping the motion con-
stant and reversing the electriflcation. As the effect of the magnetism
,of rotation was several times that of the moving electricity, and the
needle was so extremely sensitive, numerical results were extremely
hard to be obtained, and it is only after weeks of -trial that reasonably
accurate results have been obtained. But the qualitative effect, after
once being obtained, never failed. In hundreds of obseirvations extend-
ing over many weeks, the needle always answered to a change of electri-
fication of the disc. Also on raising the potential above zero the action
was the reverse of that when it was lowered below. The swing of the
needle on reversing the electriflcation was about 10- or 16- millim etres
and therefore the point of equilibrium was altered 6 or 7i millimetres.
This quantity varied with the electrification, the velocity of motion,
the sensitiveness of the needle, etc.
s

130

Senkt a. Eqwland

The direction of the action may be thus defined. Calling the motion
of the disc + when it moved like the hands .of a watch laid on the
table with its face np, we have the following, the needles being over
one side of the disc with the north pole pointing in the direction of
positive motion. The motion being +, on electrifying the disc -1- the
north pole moved toward the axis, and on changing the electrification,
the north pole moved away from the axis. With — motion and +
electrification, the north pole moved away from the axis, and with —
electrification, it moved toward the axis. The direction is therefore
that in which we should expect it to be.

To prevent any suspicion of currents in the gilded surfaces, the
latter, in many experiments, were divided into small portions by radial
scratches, so that no tangential currents could take place without suffi-
cient difference of potential to produce sparks. But to be perfectly
certain, the gilded disc was replaced by a plane thin glass plate which
could be electrified by points on one side, a gilder induction plate at
zero potential being on the other. With this arrangement, effects in
the same direction as before were obtained, but smaller in quantity,
seeing that only one side of the plate could be electrified.

The inductor plates were now removed, leaving the disc perfectly
free, and the latter was once more gilded with a continuous gold sur-
face, having only an opening around the axis of 3-5 cm. The gilding of
the disc was connected with the axis and so was at a potential of zero.
On one side of the plate, two small inductors formed of pieces of tin-
foil on glass plates, were supported, having the disc between them. On
electrifying these, the disc at the points opposite them was electrified
by induction but there could be no electrification except at points near
the inductors. On now revolving the disc, if the inductors were very
small, the electricity would remain nearly at rest and the plate
would as it were revolve through it. Hence in this case we should
have conduction without motion of electricity, while in the first experi-
ment we had motion without conduction. I have used the term

nearly at rest ” in the above, for the following reasons. As the disc
revolves the electricity is being constantly conducted in the plate so as
to retain its position. Now the function which expresses the potential
producing these currents and its differential coefficients must be con-
tinuous throughout the disc, and so these currents must pervade the
whole disc.

On the Magnetic Eeeect oe Eleoteio Convection 131

To calculate these currents we have two ways. Either we can con-
sider the electricity at rest and the motion of the disc through it to
produce an electromotive force in the direction of motion and propor-
tional to the velocity of motion, to the electrification, and to the surface
resistance; or, as Professor Helmholtz has suggested, we can consider
the electricity to move with the disc and as it comes to the edge of the
inductor to be set free to return by conduction currents to the other
edge of the inductor so as to supply the loss there. The problem is
capable of solution in the case of a disc without a hole in the centre but
the results are too complicated to be of much use. Hence scratches
were made on the disc in concentric circles about *6 cm. apart by which
the radial component of the currents was destroyed and the problem
became easily calculable.

For, let the inductor cover ^th part of the circumference of any
one of the conducting circles; then, if G is a constant, the current in
the circle outside the inductor will be -I--, and inside the area of the
inductor — On the latter is superposed the convection cur-

rent equal to -|-G- Hence the motion of electricity throughout the
whole circle is - what it would have been had the inductor covered the
whole circle.

In one experiment n was about 8. By comparison with the other
experiments we know that had electric conduction alone produced effect
we should have observed at the telescope — 5- mm. Had electric con-
vection alone produced magnetic effect we should have had + 5-7 mm.
And if they both had effect it would have been + *7 mm., which is prac-
tically zero in the presence of so many disturbing causes. Ufo effect
was discovered, or at least no certain effect, though every care was used.
Hence we may conclude with reasonable certainty that electricity pro-
duces nearly if not quite the same magnetic effect iu the case of con-
vection as of conduction, provided the same quantity of electricity
passes a given point in the convection stream as in the conduction
stream.

The currents in the disc were actually detected by using inductors
covering half the plate and placing the needle over the uncovered por-
tion; but the effect was too small to be measured accurately. To prove

183

Heket a. EowIiAKD

tMs moie thoroTighly numerical resultB ■were attempted, and, after
weeks of labor, obtained. I gi've below the last results which, from
the precan.'tions taken and the increase of experience, have 'the greatest
weight.

The magnetizing force of 'the disc was obtained from the deflection
of the astatic needle as follows. Tnming the two needles with poles
in "the same direction and observing 'the nnmber n of ■vibrations, and
then 'turning 'them opposite and finding the n'umber n' of vibrations in
"that position, we shall find, when the lower needle is the s'trongest.

X-X'

V? +

. . ( 1 )

where X' and X are the forces on the upper and lower needle re-
spectively, A the deflection, D the distance of the scale and H the
horizontal component of the earth’s magnetism. As X' and n' are very
AT" n i l the first term is nearly X — X'. The torsion of the silk fibre was
too aman to affect the result, or at least was almost eliminated by the
method of experiment.

The electricity was in the first experiment distributed nearly uni-
formly over the disc with the exception of the opening in the centre
and the excess of distribution on the edge. The surface density on
either side was

T- T

27r

. ■ ( 2 )

Y Y' bemg the dhSerence of potential between the disc and the

outside plates, ^ the thickness of the disc and B the whole distance
apart of 'the outside plates. The excess on the edge was (Maxwell’s
Electricity, Art. 196, Eq. 18),

where C is the radius of the disc.

We may calculate the magnetic effect on the supposition that, as in
the conducted current, the magnetizing force due to any clement of
surface is proportional to the quantity of electricity passing that
element in a unit of time. The magnetic effect due to the uniform
distribution has the greatest effect. Witli an error of only a small

On the Magnbtio Ebbect oe Eleotrio Conveotion 133

fraction of a per cent, -we may consider the two sides of the disc to
coincide in the centre. Taking the origin of coordinates at the point
of the disc under the needle and the centre of the disc on the axis of Z
we find for both sides of the disc, the radial component of the force
parallel to the disc,

P*' (J + ») dady

" “ V J_(o+*n/. (a’ + a? +

V J-io+t) («*+ **) b'—Zbx’

where a is the distance of the needle from the disc and J that from
the axis; N is the number of revolutions of the disc per second and
v = 28,800,000,000 centimetres per second according to Maxwell’s de-
termination. The above integral can he obtained exactly by elliptic
integrals, but as it introduces a great variety of complete and incom-
plete elliptic integrals of all three orders, we shall do best by expanding
as follows:

jSr=^^P = l!J^(ri, + J, + ri. + &o0, ... (4)

Ai = 2J^arc tan - ^ j — «log« >

= — gj- ^(s -f- b) log, — 2(7^ ,

+ ^6s’ + Oa’J + o’ ( a + &o., &c.,

w1i6r6

, = ?* .+ ?! “ , M= cd + (0 + by, iV= a» + (0 - by.

From this must be subtracted the effect of the opening in the centre,
for which the same formula will apply.

The magnetic action of the excess at the edge may be calculated on
the supposition that that excess is concentrated in a circle of a little
smaller diameter, C", than the disc; therefore,

134

Hbnbt a. Eowland

where Tc =

and jP(fc) and E(Jc) are complete elliptic

integrals of the second and first orders respectively.

The determination of the potential was by means of the spark which
Thomson has experimented on in absolute measure. For sparks of
length Z between two surfaces nearly plane, we have on the centimetre,
gram, second system, from Thomson's experiments.

F- F' = 117-5 (Z-h .0135),

and for two balls of finite radius, we find, by considering the distribu-
tion on the two sheets of an hyperboloid of revolution,

V- V = 117-5 (I + -0135) , ^

where r is the ratio of the length of spark to diameter of balls and had
in these experiments a value of about 8. In this case

F- F' = 109-6 (Z 4- -0135). (6)

A battery of nine large jars, each 48- cm. high, contained the store
of electricity supplied to the disc, and the difference of potential was
determined before and after the experiment by charging a small jar and
testing its length of spark. Two determinations were made before and
two after each experiment, and the mean taken as representing the
potential during the experiment.

The velocity of the disc was kept constant by observing a governor.
Tlie number of revolutions was the same, nearly, as determined by the
Sizes of the pulleys or the sound of a Seebeck siren attached to the
axis of the disc; the secret of this agreement was that the driving cords
wore well supplied with rosin. The number of revolutions was 61* per
second.

In such a delicate experiment, the disturbing causes, such as the
changes of the earth^s magnetism, the changing temperature of the
room, &c., were so numerous that only on few days could numerical
results be obtained, and even then the accuracy could not bo great.
The centimetre, gram, second system, was used.

Fi 7 *st Series, a = 2-05, & = 9*08, n=*697, P = 110*, H — -182
nearly, 5 = 1-68, /5=-50, (7 = 10*55, iV — 61*, v = 38,800,000,000*,
n'=*0533. O' = 10.

On the Magnetic Efeeot of Blbotbio Oonteotion

Direotion of
motion.

Bleotrifloa-
tlonof dlso.

Scale reading
In mm.

Deflection on
reversing
electrifloat^
in mm.

Length of
spark.

99-

107*6

7*26

*295

—

101*6

68*6

76*6

8-3.^

-290

68*0

97*

91*6

7*00

-283

100*

69*

65*6

6*75

•265

68*6

92*6

85*

0*75

*390

91*0

52*5

57*6

6*60

•386

61*5

82*0

76*0

5*85

*385

81*7

86*5

48*0

6*50

•375

86*5

68*0

61*0

7*00

•390

68*0

37*5

88*6

0*50

-388

36-5

Kean yalnes.

0*785

*3845

Hence

A = = •33'}' and I - -3845 .

Prom equation (1),

By calculation from the electrification we find

136

Hbnrt a. IlowLAin)

^-'’»^'=S55W=

The effect on the upper needle, X’, vas about of that on the
lower X.

Second Series. Everything the same as before except the following.
6 = 7-66, n'=-0526.

Defieotion on

Direction of
motion.

Electrifica-
tion of disc.

Scale reading
in mm.

reversing

eleotrificat'n

Length of
sparlE.

in mm.

173-5

—

165-5

7-0

•800

173-5

130-0

—

127-6

121-6

7-6

•396

—

139-0

108-6

170-5

168-0

7-35

-297

170-6

118-0

—

137-0

130-0

8-36

-370

—

137-6

Mean values.

7-50

-3966

4 = -376, ?=-2955.

Hence for this case we have from equation (1),

X- ’QdX' =

316000-

=•00000317.

And from the electrification,

TMrd Series. Everything the same as in the first series, except
6 = 8-1, «' = -0501, P = 114.

On thb Magnbtio Bfbeot ob Eiboteio Oonvbotion 137

Deflection on

Direotlon of
motion*

Electrlfioa-
tionof diso.

Scale reading
In nun.

reversing

electriflcat'n

Length of
spark.

in mm.

161*0

—

....

158*5

7.60

•287

161*0

192*0

185*5

7*26

-292

198*6

167*6

—

148*5

167-6

8*25

-295

150*0

....

186-0

192*6

186*6

7*76

-802

198-6

...

151-0

148-6

7-25

•287

—

150-5

Mean yalnes.

7-60

•2926

J = -380, Z=-a926.

For this ease from, equation. (1)

and from the electridcation

The error amounts to 8, 10 and 4 per cent respectively in the three
series. Had we taken Weber’s value of v the agreement would have
been still nearer. Considering the difGLculty of the experiment and
the many sources of error, we may consider the agreement very satis-
factory. The force measured is, we observe, about Tirhnr of the hori-
zontal force of the earth’s magnetism.

The difiterence of readings with and — motion is due to the
magnetism of rotation of the brass axis. This action is eliminated
from the result.

It will be observed that this method gives a determination of «, the
ratio of the electromagnetic to the electrostatic system of units, and if
carried out on a large scale with perfect instruments might give good
results. The value i; = 300,000,000’ metres per second satisfies the
first and last series of the experiments the best.

JBerlin, JP^ebruary 15, 1870.

NOTE ON THE MAGNETIC EFFECT OF ELECTEIC
CONVECTION

[.PMXotopUeal Magazine [5], VII, 442, 448, 1879]

Johns Hopbustb Hniteesixt, BAiiToiOBB, April 8, 1878.

To the JSditors of the Philosophical Magaisine and Journal.

Gbntlbmhn: — Some three years since, while in Berlin, I made some
experiments on the magnetic effect of electric convection, which have
since been published in the ‘ American Journal of Science ’ for Jan-
uary, 1878. But previous to that, in 1876, Professor Hdmholtz had
presented to the Berlin Academy an abstract of my paper, which has
been widely translated into many languages. But, although Helm-
holtz distinctly says, “Ich bemerke dabei, das derselbe den Plan fiir
seine (Eowland’s) Versuche schon gefasst und vollstSndig uberlegt
hatte, ala er in Berlin ankam, ohne vorausgehende Einwirkung von
meiner Seite,” yet nevertheless I now find that the experiment is being
constantly referred to as Helmholtz’s eaperiment — and that if I get
any credit for it whatever, it is merely in the way of carrying out
Helmholtz’s ideas, instead of aU the credit for ideas, design of appar-
atus, the carrying out of the experiment, the calculation of results, and
everything which gives the experiment its value.

Unfortunately for me, Helmholtz had already experimented on the
subject with negative results; and I found, in travelling through Ger-
many that others had done the same. The idea occurred in nearly
the same form to me eleven years ago; but as I recognized that the
experiment would be an extremely delicate one, I did not attempt it
until I could have every facility, which Helmholtz kindly gave me.

Helmholtz kindly suggested a more simple form of commutator than
I was about to use, and also that I should extend my experiments so
as to include an uncoated glass disk as well as my gilded vulcanite
ones; but aM else I claim as my own, — the method of experiment in all
its details, the laboratory work, the method of calculation — indeed every-
thing connected with the experiment in any way, as completely as if it had
been carried out in my own laboratory JiOOO miles from the Berlin labor-
atory. Yours truly, H. A. EowtAND.

NOTE ON THE THEOBY OF ELECTBIO ABSORPTION

[American of MathematicB, f 58-58, 18781

In experimenting with Leyden jars^ telegraph cables and condensers
of other fonns in which there is a solid dielectric, we observe that after
complete discharge a portion of the charge reappears and forms what
is known as the residual charge. This has generally been explained
by supposing that a portion of the charge was conducted below the
surface of the dielectric, and that this was afterwards conducted back
again to its former position. But from the ordinary mathematical
theory of the subject, no such consequence can be deduced, and we
must conclude that this explanation is false. Maxwell, in his ^Trea-
tise on Electricity and Magnetism," vol. 2, chap X, has shown that a
substance composed of layers of different substances can have this
property. But the theory of the whole subject does not yet seem to
have been given.

Indeed, the general theory would involve us in very complicated
mathematics, and our equations would have to apply to non-homo-
geneous, crystalline bodies in which Ohm"s law was departed from and
the specific inductive capacity was not constant; we should, moreover,
have to take account of thermo-electric currents, electrolysis, and
electro-magnetic induction. Hence in this paper I do not propose to
do more than to slightly extend the subject beyond its present state
and to give the general method of still further extending it.

Let us at first, then, take the case of an isotropic body in general, in
which thermo-electric currents and electrolysis do not exist, and on
and in which the changes of currents are so slow that we can omit
eloetro-magnetic induction. The equations then hecomc ^

in which x is the specific inductive capacity of the substance, h the

> Maxwell’s Treatise, Art. 835. ,

140

Hbnet a. Eowland

electric conductivity, Y the potential, p the voltune density of the elec-
tricity, and t the time.

The subtraction of one equation from the other gives
dY d(,Te\,dV d / .

+ 1? ^flogA\_l 4r -—=<>• W

^ dz ^ X J Ic dt X

To introduc© the condition that there shall be no electric absorption,
we must observe that when that phenomenon exists, a charge of elec-
tricity appears at a point where there was no charge before j in other
words, the relative distribution has been changed. Hence, if the rela-
tive distribution remains the same, no electric absorption can take
place. Onr condition is, then,

where c is independent of iJ, and and />' are the densities at th^ points
a;, y, «, and a/, ^ This gives

“ If = = ®

■where c is a function of t only and not of %, y, %, and jO, is the value of p
at the time < = 0. As we have

1 dTdm U ^ -^{log ^ /-flog ,

m Tfii X J dy dy\°^ X ) ^ ^ /

where m= — and n is a line in the direction of the current at the given

point, equation (1) becomes

1 dV dm 1 dp ^ _ q

m dn dn TF Ilf x ’

From equation (3)

— /’rttt

and hence

1 dY dm , c

m dn dn ° \ 4 x)

If we denote the strength of current at the point by 8, we have

Note on the Theoby of Electeio Absobption

141

S=-k

dV
~Sn '

and

1 dwi _ joj_

cm — 47rt?i® ^ a ’

( 3 )

this equation (3) gives the value of | =m at all points of the body

and at all times so that the phenomenon of electric absorption shall not
take place. As this equation makes m a function of x, y, z, 8 and t,
the relation in general is entirely too complicated to ever apply to
physical phenomena, mthout some limitation. Firstly then, as c is only
an arbitrary function of t, we shall assume that it is constant;

. 1 ^”* -1 (4:)

cm — iacff? dn 8

The most important ease is where ^ is a constant. Then

and

C = 4»rffl , 8 = 8te~’‘, p =

In this case, therefore, we see that both the electrification and the
currents die away at the rate c. The case where Ohm’s law is true and
the specific inductive capacity is constant is included in this ease, seeing
that when h and x constants their ratio, m, is constant. But

it also includes the cases where h and x both the same functions of
7 , 8, or X, y, z, seeing that their ratio, m, would be constant in this
case also.

When m is not constant, the chances are very small against its satis-
fying equation (4).

Hence, we may in general conclude, that electric absorption will ahnosl
certainly talee place v/rdess the ratio of conductivity to the specif ic inductive
capacity is constant throughout the body.

This ratio, m, may become a variable in several manners, as follows:

1st manner . — The body may not be homogeneous. This includes the
case, which Maxwell has given, where the dielectric was composed of
layers of diflerent substances.

M manner . — ^The body may not obey Ohm’s law; in this case h would
be variable.

8d manner. The specific inductive capacity, x> ^7 '^^’’‘7
electric force.

142

Hbney a. Eowland

It is to b© noted that the cases of electric absorption "which we
observe are mostly those of condensers formed of "two planes^ or of one
cylinder inside another, as in a telegraph cable. Our theory shows
that different explanations can be given of "these two cases.

The case of parallel plates does not admit of being explained, except
on the S"iipposition that m varies in the first manner above given, or in
this manner in combination "with the others, for we can only conceive
of the cond"uctivity and the specific ind"active capacity as being func-
tions of the ordinate or of the electric force. As the latter is constant
for all points be'tween the plates, m would still be constant although it
were a function of the electric force, and thus electric absorption would
not take place.

We may then conclude that in the case of parallel plates, omitting
explanations based on electrolysis or thermo-electric currents, the only
explanation that we can give at present is that which depends on the
non-homogenei"f3y of the body, and is the case which Maxwell has given
in the form of two different materials.- Our equations show that the
form of layers is not necessary, but that any departure from homo-
geneity is sufficient. It is to be noted that the homogeneity, which we
speak of, is electrical homogeneity, and that a mass of crystals with
their axes in different directions would evidently not be electrically
homogeneous and would thus possess the property in question. In the
case of glass it is very possible that this may be the case and it would
certainly be so for ice or any other crystalline substance which had
been melted and cooled.

In the case of hard India rubber, the black color is due to the particles
of carbon, and as other materials are incorporated into it during the
process of manufacture, it is certainly not electrically homogeneous.

As to the ordinary explanation that the electricity penetrates a little
below the surface and then reappears again to form the residual charge,
we see that it is in general entirely false. We could, indeed, form a
condenser in which the surface of the dielectric would be a better con-
ductor than the interior and which would act thus. But in general,
the theory shows that the action takes place throughout the mass of
the dielectric, where that is of a fine grained structure and apparently
homogeneous, as in the case of glass, and consists of a polarization of
every part of the dielectric.

To consider more fully the case of a condenser made of parallel
plates, let us resume our original equations. Without "much loss of
generality we can assume a laminated structure of the substance in

ITote on the Theoey oe Blecteio Absorption 14 S

tho direction of the plane YZ^ so that wi and will be only functions
of the ordinate x. Our equations then become

Eliminating ft we find

1 d cl (^dV\ d (T.dV\_^

di "35 \^1B) -m TTte j

Now let us make p = x and as t and x are independent, we find
on integration,

it —Pomo) = 0 ,

where is the value of p for some initial value of a?, say at the surface
of the condenser, and is an arbitrary function of t, seeing that we may
vary the charge at the surface of the body in any arbitrary manner.
This equation establishes p as a function of m and t only, and as we have

p will also be a function of these only.

Let us now suppose that at the time < = 0, the condenser is charged,
having had no charge before, and let us also suppose that the different
strata of the dielectric are infinitely thin and are placed in the same
order and are of the same thickness at every part of the substance, so
that a finite portion of the substance will have the same properties at
every part.

In this case m will be a periodic function of x, returning to the same
value again and again. As p is a function of this and of t only, at a
given time f, it must return again and again to the same value as we
pass through the substance, indicating a uniform polarized structure
throughout the body.

This conclusion would have been the same had we not assumed a
laminated structure of the dielectric. In all other cases, except that
of two planes, electric absorption can take place, as we have before*
remarked, even in perfectly homogeneous bodies, provided that Ohm^s
law is departed from or that the electric induction is not proportional
to the electric force, as well as in non-homogeneous bodies. But where*
the body is thus homogeneous, electric absorption is not due to a uni-

144 :

Hbney a. Eowland

form polarization, but to distinct regions of positive and negative
electrification.

In tlie whole of the investigation thus far we have sought for the
means of explaining the phenomenon solely by means of the known
laws of electric induction and conduction. But many of the phenomena
of electric absorption indicate electrolytic action, and it is possible that
in many cases this is the cause of the phenomenon. The only object
of this note is to partially generalize Maxwell^s explanation, leaving
the electrolytic and other theories for the future.

EESEAEOH ON THE ABSOLUTE UNIT OF ELECTEIOAL

EESISTANCE*

lAnuriom Jotwnal of ScUnee L8], Xr, 281-391, 826-886, 480-489, 1878]
PBBLIUINJkBy EbHABXS

Since the classical determination of the absolute unit of electrical
resistance by the Committee on Electrical Standards of the British
Association, two re-determinations have been made, one in G-ermany and
the other in Denmark, which each differ two per cent from the British
Association determination, the one on one side and the other on the
other side, making a total difference of four per cent between the two.
Such a great difference in experiments which are capable of consider-
able exactness, seems so strange that I decided to make a new deter-
mination by a method different from any yet used, and which seemed
capable of the greatest exactness; and to guard against aU error, it was
decided to determine aU the important factors m at least two different
ways, and to eliminate most of the corrections by the method of experi-
ment, rather than by calculation. The method of experiment depended
upon the induction of a current on a closed circuit, and in this respect,
resembled that of Kirchhofl, but it differed from his inasmuch as, in
my experiment, the induction current was produced by reversing the
main current, and in Kirchhoff’s by removing the circuits to a distance
from each other. And it seems to me that this method is capable of
greater exactness than any other, and it certainly possessed the greatest
simplicity in theory and facility in experiment.

In the carrying out of the experiment I have partly availed myself
of my own instruments and have partly drawn on the collection of the
University, which possesses many unique and accurate instruments for
electric and magnetic measurements. To insure uniformity and accur-
acy, the coils of all these instruments have been wound with my own
hands and the measurements reduced to a standard irule which was

' I am greatly Indebtod to Mr. Jacques, Fellow of the University, who Is an excel-
lent observer, for his assistance during the experiment, particularly in reading the
tangent galvanometer.

146

Hbnbt a. Bowlaijd

again compared with the standard at Washington. Unlike many Ger-
man instruments, quite jBne wire has always been used and the number
of coils multiplied, for in* this way the constants of the coils can be
more exactly determined, there is less relative action from the wire
connecting the coils, and above aU we know exactly where the current
passes.

The experiment was performed in the back room of a small house
near the University, which was reasonably free from magnetic and other
physical disturbances. As the magnetic disturbance was e limin ated
in the experiment, it was not necessary to select a region entirely free
from such disturbance. The small probable error proves that sufficient
precaution was taken in this respect.

The result of the experiment that the British Association unit is too
great by about *88 per cent, agrees well with Joule^s experiment on the
heat generated in a wire by a current, and makes the mechanical equiv-
alent as thus obtained very nearly that which he found from friction:
it is intermediate between the result of Lorenz and the British Asso-
ciation Committee; and it agrees almost exactly with the British Asso-
ciation Committee's experiments, if we accept the correction which I
have applied below.

The difference of nearly three per cent which remains between my
result and that of Kohlrausch is difficult to explain, but it is thought
that something has been done in this direction in the criticism of his
method and results which are entered into below. My value, when
introduced iato Thomson's and Maxwells values of the ratio of the
electromagnetic to the electrostatic units of electricity, caused a yet
further deviation from its value as given in MaxwelFs electromagnetic
theory of light: but experiments on this ratio have not yet attained
the highest accuracy.

Histobt

The first determination of the resistance of a wire in absolute meas-
ure was made by Kirchhofi “ in 1849 in answer to a question propounded
by Neumann, in whose theory of electrodynamic induction a constant
appeared whose numerical value was unknown until that time. His
method, like that of this paper, depended on induction from currents:
only one galvanometer was used and the primary current was measured
by allowing only a small proportion of it to pass through the galvano-

^BestimniTing der Constanten Ton wolcher die Intensltat inducirter elektrisclier
Strome abhangt. Pogg. Ann., Bd. 76, S. 412.

On the ABBOIitTTB TTnit of Blbotbioal Eesistanob 147'

meter by means of a shunt, while all the induced current passed through
it. But, owing to the heating of the wires, the shunt ratio cannot be
relied upon as constant, and hence the defect of the method. At pres-
ent this experiment has only historical value, seeing that no exact
record was kept of it in a standard resistance. However, we know that
the wire was of copper and the temperature 0® E. and that the result
obtained gave the resistance of the wire -f smaller than Weber found
for the same wire at 30® E. in 1861.

In 1861, Weber published* experiments by two methods, first by
means of an earth inductor, and second by observing the damping of a
swinging needle. Three experiments gave for the resistance of the

circuit 1903-10®, 1898-10*, and 1900-10® but it is to be noted

that a correction of five-eighths per cent was made on account of the
time, two seconds, which it took to turn the earth-inductor, and that
no account was taken of the temperature, although the material was

copper. He finds for the value of the Jacobi unit, 698- 10^ Three

SBC*

years after that, in 1863, Weber made another determination of the
specific resistance of copper.* But these determinations were more to
develops the method than for exact measurement, and it was not until
1863 * that Weber made an exact determination which he expected to
be standard. In this last determination he used a method compounded
of his first two methods by which the constant of the galvanometer was
eliminated, and the same method has since been used by Kohlrausch
in his experiments of 1870. The results of these experiments were
embodied in a determination of the value of the Siemens unit and of
a standard which was sent by Sir Wm. Thomson. As the old Siemens
units seem to vary among themselves one or two per cent, and as the
result from Thomson’s coil differs more than one per cent from that
which would be obtained with any known value of the Siemens unit,
we cannot be said to know the exact result of these experiments at the
present time. Beside which, it was not until the experiments of Dr.
Hatthiessen on the electric permanence of metals and alloys, that a
suitable material could be selected for the standard resistance.

The matter was in this state when a committee was appointed by the

>Blektrodyuami8Che Haasbestiinmnngen ; or Fogg. Ann., Bd. 8S, S. 837.

*Abli. d. KSn. Oes. d. Wissenebaften zu Gottingen, Bd. 6.

>!Sur Galvanouetrle, Gottingen, 1863. Also Abb. d. K. Ges. d. Wia. zn GSttingen,
Bd. 10.

148

Hbney a. Eowland

British Association in 1861, who, hy their experiments which have ex-
tended through eight years, have done so much for the absolute system
of electrical measurements. But the actual determ i nation of the unit
was made in 1863-4. The method used was that of the revolving coil
of Sir William Thomson, the principal advantage of which was its sim-
plicity and the fact that the local variation of the earth^s magnetism
was entirely eliminated and only entered into the calculation as a small
correction. The principle of the method is of extreme beauty, seeing
that the same earth^s magnetism which causes the needle at the centre
of the coil to point in the magnetic meridian also causes the current in
the revolving coil which deflects the needle from that meridian. When-
ever a conducting body moves in a magnetic field, currents are gener-
ated in it in such direction that the total resultant action is such that
the lines of force are apparently dragged after the body as though they
met with resistance in posing through it: and so we may regard Thom-
son's method as a means of measuring the amount of this dragging
action.

But, however beautiful and apparently simple the method may appear
in theory, yet when we come to the details we find many reasons for
not expecting the finest results from it. Nearly aU these reasons have
been stated by Kohlrausch, and I can do barely more in this direction
than review his objections, point out the direction in which each would
affect the result, and perhaps in some cases estimate the amount.

In the first place, as the needle also induced currents in the coil
which tended in turn to deflect the needle, the needle must have a very
small magnetic moment in order that this term may be small enough
to be treated as a correction. Bor this reason the magnetic needle
was a small steel sphere 8 mm. diameter, and not magnetized to satur-
ation. It is evident that in a quiescent magnetic field such a magnet
would give the direction of the lines of force as accurately as the largo
magnets of Gauss and Weber, weighing many pounds. But the mag-
netic force due to the revolving coil is intermittent and the needle must
show as it were the average force, together with the action due to
induced magnetization. Whether the magnet shows the average force
acting on it or not, depends upon the constancy of the magnetic axis,
and there seems to be no reason to suppose that this would change in
tho slightest, though it would have been better to have made the form
of the magnet such that it would have been impossible. The induced
magnetism of the sphere would not affect the result, were it not for tho
time taken in magnetization: on this account the needle is dragged

On tee Absolute Unit oe Eleotbical Eesistanob

149

Trlth the coil, and hence makes the deflection greater than it should he,
and the absolute value of the Ohm too small by a very small quantity.
The currents induced in the suspended parts also act in the same
direction. Neither of these can be estimated, but they are evidently
very minute.

TTie mere fact that this small magnet was attached to a comparatively
large mirror -vrliioh was exposed to air currents could hardly have
affected the results, seeing that the disturbances would have been all
eliminated except those due to air currents from the revolving coil, and
which we are assured did not exist from the fact that no deflection took
place when the coil was revolved with the circuit broken. In revolving
the coil in opposite directions very different results were obtained, and
the explanation of this has caused considerable discussion. As this is
of fundamental importance I shall consider it in detail.

The magnet was suspended by a single fibre seven feet long, and the
deflection was diminished by its torsion '00133. No mention is made
of the method used for untwisting the flbre, and we see -that it would
require only 3*11 turns to deflect the needle 1° from the meridian.
To estimate the approximate effect of this, we may omit from Maxwell’s
equation * all the other minor corrections and we have

QKw006<P , QKw 1

■"“*sin?>+<(<»-/9) ~ * tan <p(X + i) T'~ 0 \ nearly,

BiiX9(i+i))

where we have substituted p — /9 f or ^ in Maxwell’s equation in the
term involving t. In this equation ^ is measured from the magnetic
meridian; but let us take ^ as the angle from the point of equilibrium.
Then f = <p' + a and if^' = <p" — a, where <!'' sJid f' are for negative

rotation and <4" and f" for positive rotation and «=arc sin M-., ‘

Let

Then

r- ^

^ - OXw

/yjft — I

GR"= .

tan </'" (1 + t)

7e,= j(/e' + 7i")'

Where B' and 72" are the apparent values of the resistance as calculated
from the negative and positive rotations, and 72, is the mean of the

< < Beportg on Eleotrical Standarda,’ p. 108.

160

Henet a. Eowland

two as taken from the table published by the British Association Com-
mittee. If E is the true resistance.

OR =

sing ^
sin (f^'j

We shall then find approximately

1 + tan <(•' tan a

1 — tan 4^' tan a

When a is small compared with 4^' or 4^, and when these are also small,
we have

22 = i2/ (1 -t- a* (a* — i <^’) + Ac.).

So that by taking the mean of positive and negative rotations, the
efEect of torsion is almost entirely eliminated. Now a is the angle by
which ihe needle is deflected from the magnetic meridian by the torsion

and its value is ^^1 — nearly, when a is small, and this, in one
or two of their er^eriments, exceeds unify or a exceeds 28°. 6, which
is absurd. Taking even one of the ordinary cases where ^ = 102

and ip is about we have o= 12°* nearly, which is a value so large
that it would surely have been noticed. Hence we may conclude
that no reasonable amount of torsion in the silk fi,bre could have
produced the difference in the results from positive and negative
rotation, as has been stated by Mr. Fleming Jenkin in his ‘ Report ou
the New Unit of Electrical Eesistance.' ’

The greatest value which we can possibly assign to « which might
have remained unnoticed is which would not have affected the
the experiment to any appreciable extent.

Another source of error which may produce the difference we arc
discussing is connected with the heavy metal frame of the apparatus,
in which currents can be induced by the revolving coil. The coil
passes so near the frame-work that the currents in it must be quite
strong and produce considerable magnetic efEect. Kohlrausch has
pointed out the existence of these currents, but has failed to consider
the theory of them. Now, from the fact that after any number of
revolutions the number of lines of force passing through any pari,
of the apparatus is the same as before, we immediately deduce the

<KeportB on Electrical Standards,’ London, 1873, p. 101.

On ihb Absolute Unit oe Eleoteioal Eesistanoe 151

fact that, if Ohm’s law he correct, the algebraical smn of the ciirrents
at every point in the frame is zero, and hence the average magnetic
action on the needle zero. But although these currents can have
no direct action, they can still act by modifying the current in the
coil; for while the coil is nearing one of the supports the current
in the coil is less than the normal amount, and while it is leaving
it is greater; and although the total current in the coil is the normal
amount, yet it acts on the needle at a different angle. By changing
the direction of rotation, the effect is nearly but not quite eliminated.
The amount of the effect is evidently dependent upon the velocity
of rotation and increases with it in some unknown proportion, and
the residual effect is evidently in the direction of making the ac^on
on the needle too small and thus of increasing B. If these currents
are the cause of the different values of B obtained with positive and
negative rotation, we should find that if we picked out those experi-
ments in which this difference was the greatest, they should give
a larger value of B than the others. Taking the mean of all the
results * in which this diSerence is greater than one per cent, we find

for the Ohm 1.0033 and when it is less than one per

cent, "9966 which is in accordance with the theory, the

S6C«

average velocities being and nearly. But the individual
observations have too great a probable error for an exact comparison.

But whatever the cause of the effect we are considering, the follow-
ing method of correction must apply. The experiments show that B
is a function of the velocity of rotation, and hence, by Taylor’s theorem,
the true resistance Eo must be

B,^B (1 + Aw + Bw^ + &c.),

and when B is the mean of results with positive and negative rotations,
Bo = E (1 -1- -f- Dw* -h &c.).

Supposing that all the terms can be omitted except the first two, and
using the above results for large and small velocities, we find Bo

= -9996®“*^ But if wc roioct the two results in which the

sec. "

H In the table published by the Committee the diflPerent columns do not agree, and
I have thought It probable that the last two numbers in the next to the last column
should read 1-0082 and 1-0006 Instead of 1-0040 and -9981, and In my discussion I
have considered them to read thus.

152

Hbkby a. Eowlaitd

diflerenee of positive and negative rotations is over seven per cent,
vre find

^ g^earth£nad.

® sec.

The rejection of all the higher powers of w renders the correction
nncertain^ hut it at least shows that the Ohm is somewhat smaller
than it was meant to he, which agrees with my experiments.

It is to be regretted that the details of these experiments haye
never been published, and so an exact estimate of their value can
never be made. Indeed we have no data for determining the value
of the Ohm from the experiments of 1863. All we know is that, in
the . final result, the 1864 experiments had five times the weight of
those of 1863, and that the two results differed ‘16 per cent, but
which was the larger is not stated. Now the table of results pub-
lished in the report of the 1864 experiments contains many errors,
some of which we can find out by comparison of the columns. The
following corrections seem probable in the eleven experiments: No. 4,
second column, read 4-6376 for 4- 6275. No. 10, fourth and fifth
columns, read 1*0038 and + 0*38 in place of 1*0040 and + 0*40. No.
11, fourth and fifth columns, read 1*0065 and + 0*66 in place of 0*998^1
and — 0*19. Whether we make these corrections or not the mean
value is entirely incompatible with the statement with respect to the
1863 experiments. With the corrections the mean value of the 1864

experiments is 1 Ohm = 1*00071 and without them, using

sec.

the fourth coltuim, it is I-OOOIA With the corrections the difference
between fast and slow rotation is -6 per cent.

In the year 1870 Professor F. Eohlransch made a new determination
of Siemen’s unit in absolute measure, the method being one formed
out of a combination of Weber’s two methods, of the earth inductor and
of damping, by which the constant of the galvanometer was eliminated,
and is the same as Weber used in his experiments of 1862. His formula
for the resistance of the circuit, omitting small corrections, is

SiS'TX (A--lo)AB

(3r+£^

approximately,

where 8 is the surface of the earth inductor, T is the horizontal inten-
sity of the earth’s magnetism, K the moment of inertia of the magnet,
the time of vibration of the magnet, A the logarithmic decrement,
and A and B are the ares in the method of recoil.

On the Absolute Unit op Electrical Eesistanob 153

One of the principal criticisms I have to oflEer "with respect to this
method is the great number of quantities difficult to observe, which
enter the equation as squares, cubes, or even fourth powers. Thus 8^
depends upon the fourth power of the radius of the earth inductor.
Now this earth inductor was wound years before by W. Weber, and the
mean radius determined from the length of wire and controlled by
measuring the circumference of the layers. Now the wire was nearly
3-2 mm. diameter with its coating, and the outer and inner radii were
115- mm. and 142 mm. Hence the diameter of the wire occupied two
per cent of the radius of the coil, making it uncertain to what point
the radius should be measured. As the coil is wound, each winding
sinks into the space between the two wires beneath, except at one spot
where it must pass over the tops of the lower wires. The wire must
also be wound in a helix. All these facts tend to diminish 8 and make
its value as deduced from the length of the wire too large; and any
kinks or irregularities in the wire tend in the same direction. And
these errors must be large in an earth-inductor of such dimensions,
whore the wire is so large and many layers are piled on each other.
If we admit an error of one-half a millimetre in the radius as deter-
mined in this way, it would dimmish the value of 8^ 1-4 per cent, and
make Kohlrausch^s result only *6 per cent greater than the result of
the British Association Committee.

Three other quantities, IT, X and K, oxe very hard to determine with
accuracy, and yet T enters as a square. It is to be noted that this
earth-inductor is the same as that used by Weber in his experiment of
1862, and which also gave a larger value to the Ohm than thoso of the
British Association Committee. Indeed^ the results with this inductor
and iy this method form the only cases where the aisolute resistance of the
Ohm has teen found greater than that from the expeinments of the British
Association Committee.

There seems to be a small one-sided error in A and B which Kohl-
rausch does not mention, but which Weber, in his old experiments of
1851, considered worthy of a *6 per cent correction, and which would

diminish by 1-2 per cent. This is the error due to loss of

time in turning the earth-inductor. As Kohlrausch^s needle had a
longer time of vibration than Weberns, the correction will be much
smaller. In Weber's estimate the damping was not taken into account,
and indeed it is impossible to do so with exactness. To get some idea
of the value of the correction, however, we can assume that the current

154

Henet a. Eowlajstd

from the earth-inductor is uniform through a time and the com-
plete solution then depends on the elimination of nine quantities from
ten complicated equations, and which can only be accomplished approx-
imately. If is tilie true value of the angular velocity, as given to the
needle by the earth-inductor, and y is the velocity as deduced from the
ordinary equation for the method of recoil, I find

where A is the logarithmic decrement, e the base of the natural system
of logarithms, T the time of vibration of the needle, and t the time
during which the uniform current from the earth-inductor flows. In
the actual case, the current from the earth-inductor is nearly propor-
tional to sin t, and hence it will be more exact to substitute

in the place of The formula then becomes

1 H-

(1 + ^

■+• &c.

This modification is more exact when X is small than when it is large,
but it is sufficiently exact in all cases to give some idea of the magni-
tude of the error to be feared from this source. Kohlransch does not
state how long it took him to turn his earth-inductor, but as T = 34

seconds, we shall assume and SiS X==^ nearly, we have

Jl = 1-0008,

which would diminish the value of the resistance by -16 per cent.

As the time we have allowed for turning the earth-inductor is prob-
ably greater than it actually was, the actual correction will be less than
this.

The correction for the extra current induced in the inductor and
galvanometer, as given by Maxwell^s equation,® has been shown by
Stolctow to be too small to affect the result appreciably.

We may sum up our criticism of this experiment in a few words.
The method is defective because, although absolute resistance has th<^

dimensions of 9?^, yet in this method the fourth power of space and

‘ Electricity and Magnetism,’ art, 763.

On the Absolute Unit oe Eleoteioal Eesistanoe 155

the square of time enter, besides other quantities which are diflBicult to
dLetennine. The instruments are defective, because the earth-inductor
was of such poor proportion and made of such large wire that its
average radius was difficult to determine, and was undoubtedly over-
estimated.

It seems probable that a paper scale, which expands and contracts
with the weather was used. And lastly, the results with this inductor
and by this method have twice given greater results than anybody else
lias ever found, and greater than the known values of the mechanical
equivalent of heat would indicate.

The latest experiments on resistance have been made by Lorenz of
Copenhagen,^ by a new method of his own, or rather by an application
of an experiment of Faraday’s. It consists in measuring the difference
of potential between the centre and edge of a disc in rapid rotation
in a field of known magnetic intensity.

A lengthy criticism of this experiment is not needed, seeing that it
was made more to illustrate the method than to give a new value to
the Ohm. The quantity primarily determined by the experiment was
the absolute resistance of mercury, and the Ohm will have various
valxies according to the different values which we assume for the resist-
ance of mercury in Ohms.

One of the principal defects of the experiment is the large ratio
Letween the radius of the revolving disc and the coil in which it
revolved.

In conclusion I give the following table of results, roducod as nearly
as possible to the absolute value of the Ohm in

lopogj?. Ann., Bd. cxlix, (1878), p, 351.

u Since this was ■written, a new determination has been made by TT. E. Weber, of
Zurich, in which the different results agree with groat accuracy. The result has
been expressed in Slemen’s units, and the comparison seems to have been made
simply with a set of resistance colls and not with standards. The modern Siemen*s
■units seem to bo reasonably exact, but from the table published by the British
Association Committee in 1804, it seems that at that time there was uncertainty as

to its value. Ho obtains 1 S. U. = -onno ffroator or less than

the British Association determination, according as wo take the different ratios of
the Siemen’s to the British Association unit, ranging from -14 per cent above to 1*93
per cent below. In any case the result agrees reasonably well ■with my own. The
Apparatus used does not seem to liavo boon of the best, and the exact details are not
I^Wcn. But wooden coils to wind the wire on seem to have boeu used, which should
immediately condemn the experiment where a pair of colls is used, seeing that in
that case the constant, both of magnetic effect and of Induction, depend on the dis-
tance of the coils. It is unfortunate that sufflcleut details are not given for me to
«nter into a criticism of the experiment.

166

HBisrET A. Eowland

Date.

Observer.

Value of Ohm.

Remarks.

1849

Kircblxoff

•88 to -90

Approximately.

1851

Weber

•96 to -97

1863

(1-088

From Thomson’s unit.

} 1-076

From Weber’s value of Siemen’s unit.

1868-4

B. A. Committee.

(1-0000

Mean of all results.

j -998

Corrected to a zero velocity of coil.

1870

Kohlransob

1-0196

( -970

Taking ratio of quicksilver unit to Ohm=

1878

Lorenz

•963.

( -980

Taking ratio of quicksilver unit to Ohm=

•958.

1876

Rowland

•9912

From a preliminary comparison with the B.

A. unit.

ThHOBT OB' THE METHOD

When, a current is induced in a circuit by magnetic action of any
Faraday has shown that the induced current is proportional to the
number of lines of force cut by the circuit and inversely as the resist-
ance of the circuit. If we have two circuits near each other, the first
of which carries a current, and the second is then removed to an infinite
distance, there will be a current in it proportional to the number of
lines of force cut. Let now a unit current be sent through the second
circuit and one of strength E through the first j then, on removing
the second circuit, work will be performed which we easily see is also
proportional to the number of lines of force cut. Hence, if EM is
the work done, Q is the induced current, and B is the resistance of the
second circuit,

Q = OE^,

•where (7 is a constant whose value is unity on the absolute system.

When the current in the first circuit is broken, the lines of force
contract on themselves, and the induced current is the same as if the
second circuit had been removed to an infinite distance. If the current
is reversed the induced current is twice as great; hence in this case

Q = fiE^ or R = %M^.

Hence, to measure the absolute resistance of a circuit on this method,
we must calculate M and measure the ratio of Q to B. M is known
as the mutual potential of the two circuits ■with unit currents, and
mathematical methods are kno'wo. for its calculation.

The simplest and best form in which the wire can be wound for the

Oisr THE ABSaLTTTB TIn’it oe Bleoteioal Ebsistaitob 157

calculation of M is in parallel circular coils of equal size and of as
small sectional area as possible. Bor measuring E a tangent galvano-
meter is needed, and we shall then have

where S is the horizontal intensity of the earth^s magnetism at the
place of the tangent galvanometer, and Q the constant of the galvano-
meter.

For measuring Q we must use the ballistic method, and we have

which for very small values of X becomes

Q = ^ 2 sin i (1 + i 1 — il®) >

Rz=zM

H G' 7ctan<9

"W If T siniO^ 1 + i A —

where H' is the horizontal component of the eaxtVs magnetism at the
place of the small galvanometer, G' its constant, T the time of vibra-
tion of the needle, and X the logarithmic decrement.

The ratio of jff' to H can be determined by allowing a needle to
vibrate in the two positions. But this introduces error, and by the
following method we can eliminate both this and the distance of the
mirror from the scale by which we find and the error of tangent
galvanometer due to length of needle. The method merely consists
in placing a circle around the small galvanometer and then taking
simultaneous readings with the current passing through it and the
tangent galvanometer, before and after each experiment. Ijet « and a'
be the deflections of the tangent galvanometer and the other galvano-
meter respectively, and let G" be the constant of the circle at the point
where the needle hangs, then

tan « =

tan

and we have finally

nr G tan a' tan 0 1

= T+m:

which does not contain JET or JET^, and the distance of the mirror from
the scale does not enter except as a correction in the ratio of sin
and tan a'; and, as oand can he made nearly equal, the correction

158

Henkt a. Eowi*Ain>

of the tangent galvanometer for the length of needle is almost elimi-
nated. When the method of recoil is used, we must snbstitnte

1 +

f or the term involving and sin iA' + sin in the place of sin 0'
A' and B' being the greater and smaller arcs in that method. This is
on the supposition that 2 is small.

The ratio of ff" to 0 must be so large, say 1^,000, that it is dfflcnlt
to determine it by direct experiment, but it is found readily by measure-
ment or indirect comparison.

It is seen that in this equation the quantities only enter as the first
powers, and that the only constants to be determined which enter the
equation are Jf, Q and ff", which all vary in simple proportion to the
linear measurement. It is to be noted also that the only quantities
which require to be reduced to standard measure are M and T, and
that the others may all be made on any arbitrary scale. No correction
is needed for temperature except to M. Indeed, I believe that this
method exceeds all others in simplicity and probable accuracy and its
freedom from constant errors, seeing that every quantity was varied
except (?" and G, whose ratio was determined within probably one in
three thousand by two methods.

Having obtained the resistance of the circuit by this method, we
have next to measure it in ohms. For this purpose the resistance of
the circuit was always adjusted until it was equal to a certain German
silver standard, which was afterward carefully compared with the ohm.
This standard was about thirty-five ohms.

By this method, the following data are needed.

1. Eatio of constants of galvanometer and circle.

2. Eatio of the tangents of the two deflections of tangent galvano-
meter.

3. Eatio of the deflection to the swing of the other galvanometer.

4. Mutual potential of induction coils on each other.

5. Time of vibration of the needle.

6. Eesistance of standard in ohms.

For correction we need the following:

1. The logarithmic decrement.

2. Distance of mirror from scale.

3. Coefficient of torsion of suspending fibre.

4. Bate of chronometer.

5. Correction to reduce to standard metre.

On the Absolute Unit of Elboteioal Resistance 159

6. Variation of the resistance of German silver with the temperature.

7. Temperature of standard resistance.

8. Arc of swing when the time of vibration is determined.

9. Length of needle in tangent and other galvanometer (nearly com-
pensated by the method).

10. The variation of resistance of circuit during the experiment.

The following errors are compensated by the method of experiment.

1. The local and daily variation of the earth^s magnetism.

2. The variation of the magnetism of the needle.

3. The- magnetic and inductive action of the parts of the apparatus
on each other.

4. The correction for length of needle in the tangent galvanometer
(nearly).

5. The axial displacement of the wires in the cohs for induction.

6. The error due to not having the coils of the galvanometer and, the
circle parallel to the needle.

7. Scale error (partly).

8. The zero error of galvanometers.

Calculation of Constants

Circle . — ^For obtaining the ratio of G to G'', it is best to calculate
them separately and then take their ratio, though it might be found
by Maxweirs method C Electricity/ article 753). But as the ratio is
great, the heating of the resistances would produce error in this latter
method.

For the simple circle,

G" = 27C

where A is its radius and B the distance of the plane of the circle to
the needle on its axis.

OalvcmoiTheter for Induction Cwreni . — ^For the more sensitive galvano-
meter, we must first assume some form which will produce a nearly
uniform field in its interior, without impairing its sensitiveness. If we
make the galvanometer of two circular coils of rectangular section
whose depth is to its width as 1 08 to 100, and whose centres of sections
are at a radius apart from each other, we shall have MaxwelVs modifi-
cation of Helmholtz^s arrangement. The constant can then be found
by calculation or comparison with another coil.

160

Heney a. E0w14.Ni)

MaxweE^s formulae are only adapted to coils of small section. Hence
we must investigate a new f ormiila.“

Let N te the total number of windings in the galvanometer.

Let jB and r he the outer and inner radii of the coils.

Let X and x he the distances of the planes of the edges of the coils
from the centre.

Let a be the angle subtended by the radius of any winding at the centre.
Let J be the length of the radius vector drawn from the centre to the
point where we measure the force.

Ijet d be the angle between this line and the axis.

Let c be the distance from the centre to any winding.

Let 'W be the potential of the coil at the given point.

Then (Maxwells ^Electricity,^ Art. 695 ), for one winding,

= -r- 2 ?: 1 1 — cos a + sin® a Q[ («) {d)

+ ^ (4J w + &0-)},

and for two coils symmetrically placed on each side of the origin,

«0 = 45r I cos a — sin* a ^ Qi (“) Qi (0)

+^(4-yeu«)e4W + &c.)},

where Q 2(^)9 Q 4(^)9 denote zonal spherical harmonics, and Qi{a),

QKci) &c., denote the differential coefficients of spherical harmonics
with respect to cos a.

As the needle never makes a large angle with the plane of the coils,
it will be sufficient to compute only the axial component of the force,
which we shall call F, Let us make the first computation without
substitution of the limits of integration, and then afterward substitute
these :

and we can write

x) W + + &c.},

18 A formula involving the first two terms of my series, hut applying only to the
special case of a needle in the centre of a single circle of rectangular section, is
given by Weber in his ‘Elektrodynamlsche Maasbestimmungen inbesondere Wider-
standsmessungen,’ S. 872.

On thb ABaoLUTE Unit oe Blbotbioal Ebsistanob

161

where

ff, = x log. (r -I- VaJ* + O >

1.3.6 — 1) sin’a f ^ COS”“*a ^ COS““*a , JU. 1

i (1.2.3.. i) 5r=:F + *®-;

A-i = i,

B, = A,

' 2i — 1 (2i — 1) 2 ’

n — n (» — l)(i — 2) . . (i — 4)

^ ^ ~ 2i - 3 + — (at - 1)(27- 3) 2.4 >

D, = G , i(t-l) • . (i — 6)

' '2i-5 (ST- i)(2i - 3)(2i - 6) 2.4.6 ’

M, = &c., &c.

Substituting the limits for x, r and a, we find

o A!4-V^' + i2* , B + >/WTW

Bt = -i

r* 1 / i?

(»- + x*)i T (]

’)> (r* + X*)l X [W +^9 '

= (30X* + 7.PJ2* + 212*)

(r* + ai*)*,

.)}•

The needle consisted of two parallel laminae of steel of length, I, and
a distance, TT, from, each other. As the correction for length is small,
we may assume that the magnetism of each lamina is concentrated in
two points at a distance n I from each other, where n is a quantity to
be determined.

Hence

^ “ (72 — r'j^-^x) { (^') + -fii ^ ^4 (^) + etc. | ,

where cos ^ seeing that the needle hangs parallel to

the coils. In short thick magnets, the polar distance is about f I and
the value of n will be about f*. For all other magnets it will be between
this and unity. In the present case ti = f nearly.

As all the terms after the first are very minute, this approximation
is suflBcient, and will at least give us an idea of the amount of this
source of error.

1 B9

Hbnbt a. Eowlaito

iNDTroTiasr Cons

The mductioii coils weie in the shape of tiro parallel coils of nearly
eqxtal size and of nearly square section.

Let A and a be the mean radh of the coils. Let i be the mean
distance apart of the coils.

Let

ZufAa ,

V (A + a)* + ^ ’

Supposing the coils concentrated at their centre of section we know that

Jf. = 4:r V:2J { (4 - c) - 7- W }

where F(c) and E(c) are elliptic integrals.

If f and 37 are the depth and width of each coil, the total value of
M will be, when A = a nearly.

and we find

^ “ 1 - { + 82 "§-c*) <1 - + 20 )

^ = 3(1^): { (1 - c*) - S (2 - c*))

COBBBOJIONS _

Calling /9 and 8 the scale deflections corresponding to tan o' and sin
W, we may write our equation for the value of the resistance

i-i( /sy+i/'/sY

_Kt&Tje ^

T tan a d

where R' is the resistance of the circuit at a given 'temperature 17-0° 0.,

and K = 2?: Jf-^1 a -\-b etc.), in which JB, etc. and a, 6, etc.

are the variable and constant corrections respectively.
a. Correction for damping.

Osr THE Absolxttb Unit oe Elbctbioal Ebsista.nob 163

6. Torsion of fibre.

The needle of the tangent galvanometer was sustained on a point
and so required no correction. The correction for the torsion in the
other galvanometer is the same for j8 and d and hence only affects T.
Therefore, if i is the coefficient of torsion,

c. Rate of chronometer.

Let p be the number of seconds gained in a day above the normal
time

® 86400 •

d. Eoductioix to normal metre. The portion of this reduction which
depends on temperature must be treated under the yariable corrections.
Let m be the excess of the metre used above the normal metre, ex-
pressed in metres; then

e. Correction of T for the arc of vibration. This arc was always the
same, starting at and being reduced by damping to about

«=

where (?i and c „ are the total arcs of oscillation.

f. Correction for length of needles. Eor the tangent galvanometer,
the correction, is variable. For tho circle it is

/= . ,

where I is half the distance hetweeu the poles of the needle and A the
radius of circle. For tlio other galvanometer it is included in the
formula for Q.

A. Reduction to normal metre. As the dimension of R is a velocity
and the induction coils were wound on brass, the correction is '

A= -t"),

where y is the coefficient of expansion of brass or copper, <' tho actual
and i" the nomal temperature.

B. Correction of standard resistance for temperature. Let n be the
variation of the resistance for 1" 0,, be .the actual and V the normal
temperature 1 1' ■ ® 0 C. ; then

164

Hbitet a. Rowlant)

C. Correction, for lengtli of needle in tangent galvanometer,

0 — sin ^ (j^ ~ ®) »

wliere V is half the distance between the poles of the needle and A' is
the radius of the coil.

D. The resistance of the circuit was constantly adjusted, to the
standard, hut during the time of the experiment the change of temper-
ature of the room altered the resistance slightly; this change was
measured and the correction will be plus or minus one-half this. The
resistance was adjusted several times during each experiment. The
correction is ±1?.

Some of the errors which are compensated by the experiment need
no remark and I need speak only of the following.

UTo. 3. By the introduction of commutators at various points all
mutual disturbance of instruments could be compensated -

No. 6. In winding wire in a groove, it may be one side or the other
of the centre. By winding the coils on the centre of cylinders which
set end to end, on reversing them and taking the moan result, this
error is avoided.

No. 6. The circle was always adjusted- parallel to the coils of the
galvanometer. Should they not be parallel to the needle, G and G"
will be altered in exactly the same ratios and will thus not aHect the
result. The same may be said of the deflection of the magnet from
the magnetic meridian duo to torsion.

No. 7. jS and d both ranged over the same portion of the scale and
so scale error is partly compensated.

No. 8. The zero-point of all galvanometers was eliminated by e<iual
deflections on opposite sides of the zero-point.

IWSTHTIMBNTS

Wire and coiZs.— The wire used in all instruments was quite small
silk-covered copper wire, and was always wound in acMsurately turned '*
brass grooves in which a single layer of wire just fitted. The 8(‘parate
layers always had the same number of windings, and the wire was
wound so carefully that the coils preserved their proper shapt! through-

'* To obtain an accurate coil an accurate groove 1b neccseary, seeing tliat otlierwlse
the wire will bo hoapod up iw certain places. The circle of the tangent ^alvnnomotcr,
which was made to order In (lormany, had to ho returned in this country before u»o»
and much time was lost before llndlnff out the source of the dlfllculty.

On the Absolute TJnit of Eleotbioal Eesistanoe 165

out. STo paper was used between the layers. As the wire was small,
very little distortion was produced at the point where one layer had
to rise over the tops of the wires below. Corrections were made for
the thickness of the steel tape used to measure the circumference of
each layer ; also for the sinking of each layer into the spaces between
the wires below, seeing that the tape measures the circumference of
the tops of the wires. The steel tape was then compared with the
standard.

The advantages of small wire over large are many; we know exactly
where the current passes; it adapts itself readily to the groove without
kinks; it fills up the grooves more uniformly; the connecting wires
have less proportional magnetic effect; and lastly, we can get the
dimensions more exactly. The size of wire adopted was about No. 22
for most of the instruments.

The mean radius having been computed, the exterior and interior
radii are found by addition and substractidh of half the depth of the
coil. The sides of the coil were taken as those of the brass groove.

All coils were wound by myself personally to insure uniformity and
exactness.

Tangent galvanomeier . — This was entirely of brass or bronze, and
had a circle about 50 cm. diameter. The needle was 2-7 cm. long and
its position was read on a circle 20- cm. diameter, graduated to 15'.
The graduated circle was raised so that the aluminium pointer was on
a level with it, thus avoiding parallax. The needle and pointer only
weighed a gram or two, and rested on a point at the centre which was
so nicely made that it would make several oscillations within 1® and
would come to rest within 1' or 2' of the same point every time. I
much prefer a point with a light needle carefully made to any suspended
needle for the tangent galvanometer, especially as a raised circle can
then alone be used. The needle was suspended at a distance from any
brass which might have been magnetic. There were a scries of coils
ascending nearly as the niimbors 1, 3, 9, 27, 81, 24:3, whoso constants
were all known, but only one was used in this experiment. The proba-
ble error of a single reading was about ±1'.

Qahammeter for induction current . — This was a galvanometer on a
new plan, especially adapted for the absolute measurement of weak
currents. It was entirely of brass, except the wooden base, and was^
large and heavy, weighing twenty or twenty-five pounds. It could be
used with a mirror and scale or as a sine galvanometer. It will bo

166

Hbnbt a. Eowlaitd

necessary to describe here only those portions -which affect tho accuracy
of the present experiment.

The coils were of the form described above in the theoretical portion,
and were wound on a brass cylinder about 8-2 cm. long and 11 -C cm.
diameter in two deep grooves about 3- cm. deep and 2-6 cm. wide. The
opening in the centre for the needle was about 6-6 cm. diameter and
the cylinder was split by a saw-cut so as to diminish tho damping
effect. This coil -was mounted on a brass column rising from a gradu-
ated circle by which the azimuth of the coil could be determined by
two verniers reading to 30". Through the opening in the coil beneath
the needle passed a brass bar 96 cm. long and 2 cm. broad, carrying a
small telescope at one end. In the present experiment, this bar -was
merely xised in the comparison of the constant of the instrument with
that of another instrument. For this purpose the instrument is used
as a sine galvanometer by which a great range can be secured, and it
could be compared -with a»coil having a constant twenty-three times
less and which was used with telescope and scale.

The coils contained about five pounds of No. 22 silk-covered copper
wire in 1790- turns.

Two needles were used in this galvanometer, each constructed so that
its magnetic axis should be invariable; this was accomplished by affixing
two thin laminsB of glass-hard steel, to the two sides of a square piece
of wood, with their planes vertical. This made a sort of compound
magnet very strong for its length, and -with a constant magnetic axis.
The first needle had a nearly rectangular mirror 2-4 by 1-8 cm. on
the sides and -22 cm. thick. The other needle had a circular mirror
2-05 cm. diameter and about 1 mm. thick. The needle of tluf first was
1-27 cm. and of the second 1-20 cm. long, and the pieces of wood were
about '46 cm. and -6 cm. square respectively. The moment of inertia
of both was much increased by two small brass weights attached to
wires in extension of the magnetic axis, thus extending tho needles to
a length of 4-9 cm. and 4-2 cm. respectively. Tho total weights w(‘re
6-1 and 6-6 grams and the times of vibration ahoTxt 7-8 aiul 11 •.I
seconds. They were suspended by three single fibres of silk about •13
cm. long.

In front of the needle was a piece of plane-parallel glass. This and
tho mirrors were made by Steinhoil of Mxinich, and wcjni most perfect
in every way.

In the winding of tho coils every care was taken, seeing that a small
error in so small a coil would produce groat relative error. And for

On thb ABSoiTriE Unit ob Elbotbioal Ebsistanob

167

this reason the constant was also found by comparison with another
coil. The foEowing were the dimensions:

Mean radius 4*3212 cm.

R = 5*6212 r = 3*0212

X= 3*475565 x = *935566

E—r = 2*6000 X - a = 2*54000

N= iroo*

whence

F= 1832*25 - l*70i*§, (6) - 4*50i*^. (0) + -SOS'C, (tf) - &o.

Taking the mean dimensions of the two needles, we have

I = 1*23 , JO = *62 , n = f , cos «' = *748.

Q, (O') = + 339, Q, (<f) = - *364, = — *275 .

.*. & = 1832*25 — *083 + *071 - *002 + &o. = 1832*24.

The coil with which this galvanomLeter was compared was the large
coE of an , electro-dynamometer similar to that described in l^daxwell’s
‘ Electricity,’ Art. 726, but smaller. The coE was on Helmholtz’s
principle with a diameter of 27*6 cm., and was very accurately woxmd
on the braes cylinder. Therrf was a total of 240 windings in the coE.
The constant of this coil was 78*371 by calculation.

To eliminate the difference of intensity of the earth’s magnetism, an
observation was first made and then the positions of the instruments
were changed so that each occupied eractly the position of the other:
the square root of the product of the two results was the true result
free from error.

The coils of the galvanometer corEd be separated so that an outer
and inner pair could be used together. By comparing these parts
separately and adding the constants together we find (?. Hence two
comparisons are possible, one with the coEs together and the other with
them separate. The results were for the ratio of the constants

23*3931 and 23*40()8,

which give

(? = 1833*37 and 1833*98.

The mean result is

1833*67 ± *09,

and this includes seven determinations with two reversals of instru-
ments. This result is one part in thirteen hundred greater than found,
by direct calculation, which is to be accounted for by the smaE size of
the galvanometer coils and the consequent difficulty of their accurate
measurement. As comparison with the electro-dynamometer has such

168

Henet a. Eowland

a small probatle error, and as it is a mncli larger coil, it seems best to
give this number twice the weight of that foimd by calculation: we thus
obtain

ff = 1833 19

as the final result.

It does not seem probable that this can be in error more than one
part in two or three thousand.

Telescope^ scah, £c . — The telescope, mirrors and plane-parallel glass
were all from Steinheil in Munich, and left nothing to be desired in
this direction, the image of the scale being so perfect that fine scratches
on it could be distinguished. The telescope had an aperture of 4 cm.
and a magnifying power of 20 was used. The scale was of silvered
brass, one metre long and graduated to millimetres.

Induction coils. — coil was wound in a groove in the centre of each
of three accurately turned brass cylinders of different lengths. Two
of them only were used at a time, by placing them end to end, the ends
being ground so that they laid on each other nicely. The two coils
could be placed in four positions with respect to each other, in each of
which they were very exactly the same distance apart. This distance
for each of the four positions, was determined at three parts of the
circumference by means of a cathetometer, with microscopic objective,
reading to ^ mm. The mean of all twelve determinations was the
mean distance. In using the coils they were always used in all four
positions. The probable error of each set of twelve readings was
± -001 mm. The data are as follows, naming the coils, A, B and 0:

Mean radius of A = 13*710, of J? = 13*690, of 0 = 13*720.

Mean distance apart of A and J5 = 6*534, of A and 0 = 9*674, of
Band 0 = 11*471.

JV" =±= 154 for each coil, f = *90, = *84.

For A and B we have

Jf =3774860* — 66510*) = 3776600*

The remaining terms of the series are practically zero, as was found
by dividing one of the coils into parts and calculating the parts sepa-
rately and adding them.

For A and 0

M = 2561410* + tV (34000* — 27230*) = 2561974*

For B and 0

if = 2050600* -f yV (^'^500* — 19800*) = 2051320*

The calculation of the elliptic integrals was made by aid of the tables
of the Jacobi function, g, given in Bertrand’s ^ Trait6 dc Calcul Inte-

On the Absolute Unit of Elbctbioal Resistance 169

grale ^ as well as "by the expansions in terms of the modulus after trans-
forming them by the Landen substitution.

The Circle . — The circle whose constant we have called G" and which
was around the galvanometer whose constant was G, was a large wooden
one containing a single coil of IsTo. 22 wire/* To prevent warping, it
was laid up out of small pieces of wood with the grain in the direction
of the circumference, and was carefully turned with a minute groove
near one edge in which the wire could just lie. It was about 5* cm.
broad, 1-8 thick and 82*7 cm. diameter. As the room had no fire in
it, the circle remained perfect throughout the experiment. The wire
was straightened by stretching and measured before placing on the
circle, which last was done with great care to prevent stretching; after
the experiment it was measured and found exact to yV

The circle was adjusted parallel and concentric with the coils of the
galvanometer, but at a distance of 1-1 cm. to one side, in order to allow
the glass tube with the suspending fibre to pass. The length of wire
was 359-58 cm. which gives a mean radius of 41-31344 cm. These data
give G" = -151925. Preliminary results were also obtained by use of
another circle.

Chronometer . — To obtain the time of vibration, a marine chronometer
giving mean solar time was used. The rate was only half a second
per day.

WhecLtstone "bridge . — To compare the resistance of the circuit with the
arbitrary German silver standard, a bridge on Jenkin^s plan, made by
Elliott of London, was used. A Thomson galvanometer with a single
battery cell gave the means of accurately adjusting the resistance, one
division of the scale representing one part in fifty thousand.

Thermometers . — ^Accurate thermometers graduated to half degrees
were used for finding the temperature of the standard.

The arbitrary standard . — This was made of about seventy feet of
German silver wire, mounted in the same way as the British Association
Standard. Immediately after use, two copies, one in German silver and
the other in platinum-silver alloy, were made. It had a resistance of
about 35 ohms. The temperature was taken as 17® 0.

To obtain the accurate resistance of this standard in ohms, I had two*
standards of 10 ohms and one of 1, 100, and 1,000 ohms. The 1-ohm,
and one of the 10-ohm standards, were made by Elliott of London, and

14 In another part oi my paper I have criticised the use ol wooden circles lor coil,
but it is unobjectionable in the case ot a single wire, especially when the needle is
suspended near its centre.

170

Henet a. Eowland

the others by Messrs. Warden, Muirhead and Clark of the same place*
But on careful comparison I found that Warden, Muirhead and Clarkes
10-ohm standard was 1* 00171 times that of Messrs. Elliott Bros. On
stating these facts to the two firms I met no response from the first
firm, but the second kindly undertook to make me a standard which
should be true by the standards in charge of Professor Maxwell at
Cambridge.” At present I give the result of the comparison with
these standards, as well as some others, and also with a set of resistance
coils by Messrs. Elliott Bros.

Gommutators, — TSo commutators except those having mercury con-
nections were used, and those in the circuit whose resistance was deter-
mined were so constructed as to offer no appreciable resistance. The
commutator by which the main current was reversed, could be operated
in a fraction of a second, so as to cause no delay in the reversal.

Connecting mm.^These were of No. 22 or No. 16 wire and were all
carefully twisted together. The insulation was tested and found to be
excellent.

Inductor for damping , — This has already been described in my first
paper on ^Magnetic Permeability,^ and merely consisted ojE a small
horse-shoe magnet with a sliding coil, which was introduced into the
secondary circuit. By moving it back and forth, the induced current
could be used to stop the vibrations of the needle and make it stationary
at the zero point. This is necessary in the method where the first throw
of the galvanometer needle constitutes the observation, but in the
method of recoil it is not necessary to use it very often. I prefer the
method of the first throw as a general rule, but I have used both
methods.

This method of damping will be found much more efficient than that
of the damping magnet as taught by Weber, and after practice a single
movement will often bring the needle exactly to rest at the zero point.

Arrangement of apparatus , — Two rooms on the ground floor of a
small building near the University were set aside for the experiment,
making a space 8 m. long by 3-7 m. wide. The plan of the arrange-
ment is seen at Fig. 1. The current from the battery, in the Univer-
sity, entered at A, the battery being eighteen one-gallon cells of a
chromate battery, arranged two abreast and eight for tension. The

As tills is nearly a year since, and as I cannot tell when the standard will arrive,
I now pnhlish the results as so far obtained, hoping to make a more exact comparison
in future.

On xhb Absoitjtb XJnii ob Ilboteioal Eesibtanob l^l

resistance of the circuit vas about 20 ohms, and of the whole battery
about i ohm, thus insuring a reasonably constant current.

At B some resistance could be inserted by withdrawing plugs so as
to vary the current.

At G is the tangent galvanometer with commutator on a brick pier.
The nearness of the commutator produces no error, seeing that we only
wish to determine the ratio of two currents. The effect of currents in
the commutator was, however, vanishingly small in any case.

At D is the principal commutator which reversed the current in the
induction coils, L, or in the circle, F, when it was in the circuit.

Fio. 1.

The secondary circuit included the induction coil, L, the damping
inductor, M, and the galvanometer (?.

At E was the Jenkin’s bridge, with standard at P, in a beaker of
water, and a Thomson galvanometer at J K. The secondary circuit
could be joined to the bridge by raising a U-shaped piece of wire out of
the mercury cups.

The telescope and scale, JE, were on a heavy wooden table, and the
two galvanometers on brick piers with marble tops.

A row of gas-burners at Q illuminated the silvered scale in the most
perfect manner.

Adjustments and tests . — ^The circle, F, must be parallel to coils of
galvanometer, Q. The circle and coils of galvanometer were first
adjusted with their planes vertical and then adjusted in azimuth by

172

Hbnby a. Bowland

measurement from the end of the bar, 22, to the sides of the circle, F.
The adjustment was always within 30', which would only cause an error
of one part in 25000.

The needle must hang in the magnetic meridian by a fibre without
torsion, and the coils must be parallel to it. These adjustments were
carefully made, but, as has been shown, the error from this source is
compensated.

The needle must hang in the centre of the galvanometer coils and
on the axis of the circle. The error from this source is vanishingly
small.

The scale must be perpendicular to the line joining the zero point
and the galvanometer needle, it must be level and not too much below
the galvanometer needle. All errors from this source are partially or
entirely compensated by the method of experiment.

The induction coils, L, must be horizontal, and at the same level as
the two galvanometers, so as not to produce any magnetic action on
them. The error from this source is exactly compensated by this
method of experiment, but could never amount to more than 1 part in
2000.

The tangent galvanometer should have the plane of its coils in the
magnetic meridian, but all errors are compensated.

The connecting wires must be so twisted together and arranged as
to produce no magnetic action, but tests were made in all cases where
the error was not compensated, and found to be practically zero. The
insulation of all coils, wires and commutators was carefully tested.

Method of experiment , — As has been stated before, the method gener-
ally used was that of the first throw of the needle, though the method
of recoil was also used. Por the successful use of the first method a
quickly vibrating needle and the damping inductor are indispensable,
seeing that with a slow moving needle we can never be certain of its
being at rest. By this method it is not necessary to have the needle
at rest at the zero point, but, if it vibrates in an arc of only a millimetre
or two, we have only to wait till it comes to rest at its point of greatest
elongation on either side of the zero point and then reverse the commu-
tator. The error by this method is in the direction of making the
throw greater in proportion of the cosine of the phase to unity. The
smallest throw used was 100 mm. Hence, if the needle vibrated
through a total arc of 2 mm., the error would be 1 in 17,000. In reality
the needle was always brought to rest much more nearly than this.

The method of recoil was used once with the needle vibrating in 7*8

On the AbsoiiXtie Unit oe Elboteioai. Eesistanob 173

secoudB, but the time of vibration •was too short and another needle was
constructed vibrating in 11' 5 seconds, ■which was a sufdciently long
period to be used successfully after practice.

There seems to be no error introduced by the time taken to reverse
the commutator in the method of recoil, seeing that the breaking of
the current stops the needle and the making starts it in the opposite
direction. As the time was only a fraction of a second the error is
minute in any case.

While the current is broken in the reversal, the battery may re-
cuperate a little and there is also some action from the extra current,
but there seems to be no doubt that long before the four or six seconds
which the needle takes to reach its greatest elongation everything has
again settled to its normal condition and the curreht resumes its
original strength. Hence the error from these sources may be con-
sidered as vanishingly small.

Some experiments were made by simply breaking the current and
they gave the same result as by reversal.

The following is the order of observations corresponding to each

experiment.

Ist. The time of vibration of needle was observed.

2d. The current was passed around the circle, y, so as to observe

and a. Simultaneous readings were taken at the two galvanometers.
The commutator at the tangent galvanometer was then reversed and
readings again taken. After that the commutator to the circle was
reversed and the operation repeated. This gave four readings for the
circle and eight for the tangent galvanometer, as both ends of the
needle were read. In some cases these were increased to six and twelve
respectively. This operation was repeated three times -with currents
of different strengths, constituting three observations each of a and
To eliminate any action due to the induction cods, they were sometimes
connected in one way and sometimes in the opposite way.

3d. The resistance of the circuit was adjusted equal to the arbitrary

standard.

4th. The circle, F, was thrown out of the circuit and the observations
of 6 and 8 begun. Two throws, 8, one on either side of zero were
observed and one reading of 6 taken. The commutators at s and G
were then reversed, and the operation repeated. This whole operation
was then repeated with currents of three different strengths. The
position of the two induction coils was now reversed and observations
again made with the three currents. The resistance was now com-

174

Hbnet a. RawLAND

pared -with the standard, the difference noted, and the resistance again
adjusted. The ohservations were completed by turning the induction
coils into the two other positions which they could occupy with respect
to each other, followed hy another comparison of resistance with
standard.

6th. Observations of a and ^ were again made as before.

6th. The time of vibration was again determined.

The observations as here explained furnished data for three compu-
tations of the resistance of the circuit, .one with each of the three cur-
rents. In each of these three computations, a was the mean of 16
readings, ;8 of 8 or sometimes 12, d of 16 and d of 16. In using the
method of recoil nearly the same order was observed.

The time of vibration was determined by allowing the needle to
vibrate for about ten seconds and making ten observations of transits
before and after that period. During the experiment, I usually ob-
served at the telescope and Mr. Jacques at the tangent galvanometer.

The methods of obtaining the corrections require no explanation.

Rbsthts

The constat corrections are as follows for the first needle.

a = - = - *00711 .

5 = -J< = — -00020,

c = — -000006,

d= -H *000074 at 20-® 0.

/= + -00003,

a + b +.c + d.+ e+f= — -00718.

For method of recoil it becomes — 00016.

Hence for A and B, log K = 11-4636030
Hence for A and O', log A" = 11-2852033
Hence for B and C, log K = 11-1886619
For method of recoil using A and B, log E = 11-4666630.

For second needle and method of recoil, j,

a = — i J= - *000050 ,

5 = -}^=--00026,

* c = — -000006 ,

. d.= -I- *000074,

TABLE OE BESULTS

On" the Abadlitte Unit oe Elbotbioal Eesi^tanob 175

84-1T93±0070

176

HbIS-ET a. EoWIxAJS^D

e = + -00003,

/=+ -00003,

a + J + c4-^? + «-F/= — *00017 .

For A and J5, log JE' = 11-4566587
For A and (7, log £' = 11-2882590
For B and C7, log £ = 11-1917176

The distance of the mirror from the scale varied between 192*3 and
193-5 cm.

Should we reject the quantity 34-831 in the third experiment so as
to make the mean result of that experiment 34-744 instead of 34-773,
we should obtain as a mean result of the whole

34-7156 ± -0053,

which has a less probable error than when the above observation is re-
tained. The number of plus and minus errors are also more nearly
equal and the greatest difference from the mean 1 part in 1100.
However the two results do not differ more than 1 part in 10,000.

We shall take

R = 34-719 ± -007 at 17-° 0 .

second.

as the final result.

DiSOtlSSIOlT

On glancing over the table ve see that the number of negative errors
greatly exceed the number of positive, but, if ■we take only the four
errors which are greater than 1 part in 5,000, we shall find two of them
negative and two positive.

Combining the results with the different coils we have

il and B 34-696 ± -005

A and G 34-744 ± -Oil

J? and O' 34-716 ± -007

Had we no other results to go by, we might suppose that the value of
M might not have been found as exactly for these coils as we have
supposed them to be. But if we include the preliminary results re-
jected on account of the imperfect circle used, we shall find

,4 and B 34-704 ± -006

4 and 0 34-718 ± -017

B and 0 34-758 ± -016

which has the greatest error in an entirely different place.

Prom the first series the probable error of each determination of M
is 1 in about 2,000. But as this includes the experimental errors which

On the AssoLtriB Unit oe Elbotrtoal Eesistanob IT’?

are about equal to injVirj the real probable error of M roust be about
1 part in 2,600. The number of observations is however too small for
an exact estimate of the probable errors.

Taking the results with currents of different strengths, we find

For strongest current 34-716

For medium current 34-716

For weakest current 34-727

which are almost perfectly accordant. Taking the results from the
method of recoil and the ordinary method, we find

For ordinary method 34-726 ± -010

For method of recoil 34-705 ± -006

If the probable error is subtracted from the first and added to the
second they will very nearly equal each other. Hence the difference is
probably accidental. Indeed, by the combination of the results it does
not seem possible to find any cosistant source of error, and therefore
the errors should be eliminated by the combination of the results.

Xn the final result

12 = 34-7192 ± -0070

the probable error, ± -0070, includes all errors except the ratio of Q
to Q". We may estimate the probable error of ff at ± and of Q"

ait ± nj^jTc.

Hence the final probable error of B, including all variables, is ± Tjionir
or ± -04 per cent,

or 12 = 34-719 ±-015.

The probable error of the British Association determination was ± -08
per cent, not including the probable error of the constants; and of Kohl-
rausch’s determination ± -33 per cent, including constant errors. ,

COHPAEISON WITH THE OHM

The difficulty in obtaining proper standards for comparison has been
explained above and ! shall have to wait until the arrival of the new
standard before making the exact comparison. At present I give the
following results, which seem to warrant the rejection of Messrs. BEiott
Bros’. 10-ohm standard and to make that of Messrs. Warden, Muirhead
and Clark correct. I shall designate the coils by the letter of the firm
and by the number of ohms. Experiment gave the folio-wing results:
W (10) = 1-00171 X B (10), experiment of June'S, 1877.

W (10) = 1-00166 X B (10), experiment of Feb. 23, 1878.

W (1,000) :W (100):: W (10): -999876 E (1), experiment of Febru-
ary 23, 1878.

.178

Henry A. Eowland

ITow the greatest source of error in making coils is in passing from
the unit to the higher numbers. As the reproduction of single units
is a very simple process the single ohm is without much doubt correct,
and as the above proportion is correct within one part in 8,000 of what
it should be, it seems to point to the great exactness of the standards
then used, seeing that the exactness of the proportion could hardly have
been accidental. It is also to te noted that Messrs. Warden, Muirhead
& Clarkes 10-ohm standard agreed more exactly with a set of coils by
Messrs. Elliott Bros, than their own unit E (10).

The resistance of my coil as derived from the different standards is

as follows:

Prom Elliott Bros, resistance, coils 34*979 ohms.

Prom Elliott Bros. 10-ohm standard , 35*083 ohms.

Prom W., M. & C.'s 10-ohm standard ..35*024 ohms.

Prom W., M. & C.^s 100-ohm standard 35*035 ohms.

These give for my determination the values of the ohm as follows :

Prom Elliott Bros, resistance coils *99257

sec.

From Elliott Bros. 10-ohiu standard -98963 “

Prom W., M. & 0/s lO-ohm standard -99199 "

From W., M. & O.’s lOO-ohm standard -99098 “

For the reasons given above I accept the mean of the last two resnlts

as the value of the ohm.

To preserve my standard I have made two extra copies of it, the one
in German silver and the other in platinum silver alloy. The com-
parisons are given below. No. 1 is in German silver and the other in
platinum silver alloy. The temperature is 17-“ C.

No. 1 1-00034

No. 1 1-00099

No. II -99630

No. II -99939

These are the values of the copies in terms of the original standard

whose resistance is 34-719

see.

From these results it would seem that the German silver of which
the standard and No. I were composed was perfectly constant in resist-
ance. The wire has been in my possession for several years and seems
to have reached its constant state.

The final result of the experiment is

1 ohm = -9911

June, 1877.
Feb., 1878.
June, 1877.
Feb., 1878.

sec.

ON PEOFBSSOES AYETON AND PEEEY’S NEW THEOEY OP
THE BAETH’S MAGNETISM, WITH A NOTE ON A NEW
THEORY OP THE AURORA*

Magazine, [6], YXII, 103-100, 1879. Proeeedinge of the Phytieal Soeieig,
m, 98-98, 1879]

Some years ago, wMle in Berlin, I proved by direct experiment that
electric convection produced magnetic action; and I then suggested to
Professor Helmholtz that a theory of the earth’s magnetism might be
based upon the experiment. But upon calculating the potential of
the earth required to produce the effect, I found that it 'was entirely
too great to exist without producing violent perturbations in the planet-
ary movements, and other violent actions.

I have lately read Professors Ayrton and Perry’s publication of the
same theory; and as they seem to have arrived at a result for the
potential much less than I did, I have thought it worth while to publish
my reasons for the rejection of the theory.

The first objection to the theory that struck me was, that not only
the relative motion but also the absolute motion through space of the
earth around the sun might also produce action. And to this end I
instituted an experiment as soon as I came home from Berlin.

I made a condenser of two parallel plates with a magnetic needle
enclosed in a minute metal box between them; for I reasoned that, when
the plates were charged and were moved forward by the motion of the
earth around the sun, they would tlicn act in opposite directions on
the enclosed needle, and so cause a deflection when the electrification
of the condenser was reversed. On trying the experiment in the most
careful manner, there was not the slightest trace of action after all
sources of error had been eliminated.

But the experiment did not satisfy me, as I saw there was some
electricity on the metal case surrounding the needle. And so I attacked
the problem analytically, and arrived at the curious result that if an
electrified system moves forward without rotation through space, the

1 Bead before the Physical Society, June 29th.

180

Hbntet a. EowIiAND

magnetic force at any point is dependent on the electrical force at that
same point — or, in other words, that all the equipotential surfaces have
the same magnetic action. Hence, when we shield a needle from elec-
trostatic action, we also shield it from magnetic action.

This theorem only applies to irrotational motion, and assumes that
the elementary law for the magnetic action of electric convection is the
same as the most simple elementary law for closed circuits. Hence we
see that, provided the earth were uniformly electrified on the exterior
of the atmosphere, there would he no magnetic action on the earth s
surface due to mere motion of translation through space.

In calculating the magnetic action due to the rotation, I have taken
the most favorable case, and so have assumed the earth to he a sphere
of magnetic material of great permeability, [jl. It does not seem prob-
able that it would make much dijBEerence whether the inside sphere
rotated or was stationary; or at least the magnetic action would be
greatest in the latter case; and hence by considering it stationary we
should get the superior limit to the amount of magnetism.

Let a be the radius of the sphere moving with angular velocity w,
and let c be its surface-density in electrostatic measure, and n the ratio
of the electromagnetic to the electrostatic unit of electricity. Then the
current-function will be

ip^ — C sin^d^^ = ^ cos 0 .

n J ^

Hence (Maivell’s ‘ Treatise/ § 673) the magnetic potential inside the
sphere is

3 = ^ — war co^ 0,

3 n

and outside the sphere

/'»/ A ^ mmmmA COS 0

=4 7r - wcr—ji- .

^ n r

The magnetic force in the interior of the sphere is thus

F=%ic-^wa,

or the field is uniform. I£ the electric potential of the sphere on the
electrostatic system is Y, we may write

which is independent of the dimensions of the sphere.

Atbtok and Pbket’s Theory oe the Barth’s Magnetism 181

In this uniform field in the interior of the sphere, let a smaller
sphere of radius a' be situated; the potential of its induced magnetiza-
tion mil be

Hence the expression for the potential for the space between the two
spheres will be

and outside the electrified sphere it will be

^(®‘ + ^ •

Let us now take the most favorable case for the production of mag-
netism that we can conceive, making a' = a and = we then have

= -!L Fa» 5^-^,

n r* ^

which is the potential of an elementary magnet of magnetic moment

-H. Fo*.
n

But Qauss ’ has estimated the magnetic moment of the earth to be

3-3093a*.

on the millimetre mg. second system. Hence, we have

F= 3-3092

for the potential in electrostatic units on the mm. mg. second system.
In electromagnetic units it is thus

F, = 3-3092 ^ ;

and hence in volts it is this quantity divided by 10'^.

As the earth makes one revolution in 23" 66' 4", or in 86164 seconds,
we have

86164’

and

n, = 299,000,000,000 “ millims. per second.

* Taylor’s Sclent. Mem., vol. 11, p. 225.

> From a preliminary calculation of a new determination made with the greatest
care, and having a probable error of 1 In 1800.

182

Hbnbt a. EOWIAMT)

Hence the earth, must be electrified to a potential of about

41 X 10” volts*

in order, under the most favorable circumstances, to account for the
earth’s magnetism. This would be sufficient to produce a spark in
atmospheric air of ordinary density of about

6,000,000 miles!

Professors Ayrton and Perry have only found the potential 10® volts,
or 400,000,000 times less than I find it.

It was this large quantity which caused me to reject the theory; for
I saw what an immense effect it would have in planetary perturbations;
and I even imagined to myself the atmosphere fiying away, and the
lighter bodies on the earth carried away into space by the repulsion.
And, doubtless, had not Professors Ayrton and Perry made some mis-
take in their calculation by which the force was diminished 16 x 10^*
times, they would have feared like results.

For according to Thomson’s formula, the force would be equal to a
pressure outwards of

F»

^ ’

which amounts to no less than

1,800,000 grms.

per square centimetre! or 10,000 kil. per square inch! Such an electro-
static force as this would undoubtedly tear the earth to pieces, and dis-
tribute its fragments to the uttermost parts of the universe. If the
moon were electrified to a like potential, the force of repulsion would
be greater than the gravitation attraction to the earth, and it would
fly off through space.

For these reasons I rejected the theory, and now believe that the
magnetism of the earth still remains, as before, one of the great mys-
teries of the universe, toward the solution of which we have not yet
made the most distant approach.

^That this Is not too groat may be estimated from my Berlin experiment, where a
disk moving 5,000,000 times as fast as the earth with a potential of 10,000 volts,
produced a magnetic force of of the earth’s magnetism,

5,000,000 X 10,000 X 50,000=2,600,000,000,000,000,
which is of the same order of magnitude as the quantity calculated, namely 61 x
10*», It can be seen that this reasoning is correct, because the formulas show that
two spheres of unequal sisso, rotating with equal angular velocity and cliarged to the
same potential, produce the same magnetic force at similar points In the two systems.

Ayrton- and Perry's Theory oe the Earth's Magnetism: 183

Ir connectiOH with the theory of the earth’s magnetism, I had also
framed a theory of the Aurora which may still hold. It is that the
earth is electrified, and naturally that the electricity resides for the
most part on the exterior of the atmosphere — and that the air-currents
thus carry the electricity toward the poles, where the air descending
leaves it — and that the condensation so produced is finally relieved
by discharge.

The total effect would thus be to cause a difference of potential be-
tween the earth and the upper regions of the air both at the poles and
the equator. At the poles the discharge of the aurora takes place in
the dry atmosphere. At the equator the electrostatic attraction of the
earth for the upper atmospheric layers causes the atmosphere to be in
unstable equilibrium. At some spot of least resistance the upper atmos-
phere rushes toward the earth, moisture is condensed, and a conductor
thus formed on which electricity can collect ; and so the whole forms a
conducting system by which the electric potential of the upper air and
the earth become more nearly equal. This is the phenomenon known
as the thunderstorm.

Hence, were the earth electrified, the electricity would be carried to
the higher latitudes by convection, would there discharge to the earth
as an aurora, and passing back to the equator would get to the upper
regions as a lightning discharge, once more to go on its unending cycle.
I leave the details of this theory to the future.

Baltimore^ May 80, 1870,

Appmiix , — Since writing the above. Professors Ayrton and Perr/s
paper has appeared in full; and I am thus able to point out their error
more exactly. Their formula at the foot of page 400 is almost the
same as mine; but on page 407, in the fourth equation, the exponent of
n should be + ^ instead of — which increases their result by about
600,000,000, and makes it practically the same as my own.

MetUrdam^ Xtily 18.

Oir THE •n TAMA QEETIO COHSTAHTS OF BISMUTH AND
CALC-SPAE IN ABSOLUTE MEASUEE

{Americm J’oumal of Science [3], XVII2, 860-871, 1879]

Part I. — H. A. Rowland

Since my experimeiits on tlie magnetic constants of iron, nickel and
cobalt, I baye songlit the means of determining those of some diamag-
netic substances, and to that end have described a method in this
Journal for May, 1875 (vol. ix, page 367). As Mr. Jacques, Fellow of
the University, was willing to take np the experimental portion, I have
here worked up the subject more in detail and brought the formulae
into practical shape. ITo experiments have been made on this subject
so far, but some rough comparisons with iron have been made by
Becquerel, Plucker and Weber. But as iron varies so greatly, and as
the methods of experiment are inexact, we cannot be said to know
much about the subject. As, however, the relative results of these
experiments and those of Faraday can be accepted as reasonably exact
for diamagnetic substances and weak paramagnetic ones, it is only
necessary to make a determination of one substance such as bismuth,
and then the rest can be readily found. But as bismuth is very crys-
talline it is necessary to make our formulae general, unless we use bis-
muth in a powder, which would introduce error.

The general method of experiment has been indicated in the paper
before referred to, but I may here state that it consists in counting
the number of vibrations made by a bar hung in the usual manner
between the poles of an electromagnet. The distribution of the mag-
netic force in the field being known, we can then calculate the force
acting on the body, and the comparison of this with the time of vibra-
tion gives us the means of determining the constant sought. But I
will leave the more exact description to be given by Mr. Jacques in the
experimental part.

Diamaqnbtio Constants of Bismuth and Calo-Spab 185

Ezplokation of Field

The first operation to be performed is to find a formula to express
the force of the field at any point, and an experimental moans of deter-
mining it in absolute measure. The magnet used was one on the
method of Euhmkorff, and hence the field was nearly symmetrical
around the axis of the two branches, and also with respect to a plane
perpendicular to the axis at a point midway between its poles. Should
any want of symmetry exist by accident, it will be nearly neutralized
in its effect on the final result, seeing that the diamagnetic bar hangs
symmetrically.

The proper expansion of the magnetic potential for this case is
therefore a series of zonal spherical harmonics, including only the un-
even powers. Hence, if V is the potential,

V= AjQ/r + + A,Q,t* 4- etc., .... (1)

where r is the distance from the centre of symmetry, etc.,

are the spherical harmonics with respect to the angle between r and
the axis, and Aj, A,,^, A^, etc., are constants to be found by experi-
ment. The only method known of measuring a strong magnetic field
with accuracy is by means of induced currents, and in this case I have
used a modification of the method of the proof plane as I have described
it in this Journal, III, vol. x, p. 14. In the method there described the
coil was to be drawn rapidly away from the given point: in the present
case the coil was moved along the axis, thus measuring the difference
of the field at several points; on tlien placing it at the centre and
drawing it away, the field was measured at that point. The field at
the other points along this axis could then be found by adding the
measured difference to this quantity. This method is far more accu-
rate than the direct measurement at the different points.

When a wire is moved in a magnetic field the current induced in it
is equal to the change of its potential energy, supposing it to transmit
a unit current, divided by the resistance of the circuit. The potential
energy of a wire in a magnetic field is (Maxwell’s Elec., Art. 410),

which is simply the surface integral of V over any siirfaco whose edge
is in the wire.

In the present case, take the axis of x in the direction of the axis of
the poles and the surface, fif, parallel to the piano TZ, and lot p be the

186

Hen-bt a. Eowland

distance in this plane from the centre of the coil ■we are calculating.
Then

for a single circle.

From (1) ^ = Il(i+l) A,^ ,r^Q,

and /,» = *» — ij ; ^ >

where M = COS

P = - 2*£e'+»r (t + 1) ^ ,

P = 3V^U,+x^^

For a circle of rectangular section we m-ust obtain the mean value of
this q'uantity throughout the section of the coil.

•'Po— .if

Pdx dp ,

where a:, and po *1^® values of x and p at the centre of section and
sy and $ are the width and depth of the groove in which the coil is
wound. We can calculate this quantity best by the formula of Maxwell
(Electricity, Art. 700),

ilf = P. +

^Pt es j

%’•)

+ etc.

Thus we finally find

M= + + i + i (5/.* - 3) + i .^‘(1- /*“))

+ + eto.j W

It is by aid of this equation that we find the coefficients A,y
etc. in the expansion of the magnetic potential, V. For, let the coil
he moved in the field from a position where M has the value M' to
where it has the value M" : then if the coil he joined to a galvanometer
the current induced w’ill he equal to

J/' - Af"

whore R is the resistance of the circuit. If an earth inductor is in-
cluded in the circuit whose integral area is E, when it is reversed the

current is where II is the component of the earth^s magnetism

Diamagnetic Constants oe Bismtith and Calo-Spab 187

perpendicular to the plane of the inductor. The current as measured
by the galvanometer in the first case will be C sin ^ 5 (1 + and in
the second (7 sin i D (1 -j- where 0 is the constant of the galvano-
meter and k is the logarithmic decrement.

Hence

= (7 sin J- (1 + i >1) ,

=Cf8in}D(l + i>l),

sm iJ>

la this "way yre can ohtaia a series of equations containing A^, A,,,,
etc., and can thus find these by elimination.

This completes the exploration, and we have as a result a formula
giving the magnetic potential of the field in absolute measure through-
out a certain small region in which we can experiment.

The next process is to consider the action of this field upon any body
which we may hang in it.

CRYSTAnLINB BoiTT IIT MaQNEXIO FiBLD

Let the body have such feeble magnetic action that the magnetic
field is not very much influenced by its presence. In all crystalline
substances we know there exist in general three ax:es at right angles
to each other, along which the magnetic induction is in the direction of
the magnetic force. Let ki, fcj and be the coefficients of magnetiza-
tion in the directions of those axes and let a set of coBrdinate axes be
drawn parallel to those crystalline axes, the coordinates referred to
Vhich are designated by af, if and z', and the magnetic components of
the force parallel to which are X', Y' and Z'.

The energy of the crystalline body will then bo

E--}tffSqefK'' + da/dy'rfz'

In moat cases it is more convenient to refer the equation to axes in
some other direction through the crystal. Lot these axes be X, Y, Z.

Then

x—a/a +if'^ +s^Y
?/= afa' +y'li'

2 = a/ a" + y'^' +
dV dV . dV , . dV „

188

Hbnet a. Eowlani)

Hence

Z' z=Za+Ya' + Za"

= XyJ+ F/J'+Z/S"

Z' =Zr+T-/+Zr"

wliere a, y; and a", /9", f are the direction cosines of the

new axes with reference to the old.

We then find

+ V'O + + h^rY) + %XZ{k^aa^^ + + *3^") +%rZ

+^3)S'y9" dy dz

The most simple and in many respects the most interesting cases
are when the crystal has only one optic or magnetic axis. In this
case jfca = *?8-

Hence

+ Y'^-^Z^)1c^ + (Xa -I- Pit' + Z<ify(h^-~Jc^ )dx dy dz

where a, a! and are the direction cosines of the magnetic axis with
respect to the coordinate axes.

The first case to consider is that of a mass of crystal in a uniform
magnetic field. The magnetic forces which enter the equation are
those due to the magnetic action of the body as well as to the field in
which the body is placed. In the case of yery weak magnetic or
diamagnetic bodies the forces are almost entirely those of the field alone.
Hence in the case under consideration we may put P = 0 and P = 0.

Hence

((*1—^2) + *2) dy

and if v is the volume of the body

X^ ((*i“* 2 ) d + h) V .

As this expression is the same at all points of the field there is no
force acting to translate the body from one part of the field to another.
The moment of the force tending to increase ^ , where ^ = cos"V>t, is

— ^ = V JT* sin tp .

By observing the moment of the force which acts on a crystal placed
in a uniform magnetic field we can thus find the value of k^ — Tc^ or
the difference of the magnetic constant along the axis and at right
angles to it. The differences of the constants can also be found in the
case of crystals with three axes by a similar process. .

The next case which I shall consider is that of a bar hanging in a

Diamagnetic Constants oe Bismuth and Calc-Spab 189

magnetic field. ‘Let the field be symmetrical around an horizontal axis,
and also with reference to a plane perpendicular to that axis at the
centre. If the bar is yery long with reference to its section and a
plane can be passed through it and the axis we must have Z — 0, and
the equation becomes

E=-hfff{{Z*+ r*) *,+(Xa+ Fa')’ (k,-Tc;))dxdydz .

Let the axis of X coincide with the long axis of the bar, as this will
in the end lead to the most simple result, seeing that we have to inte-
grate along the length of the bar.

Let r be the length along the bar from the centre to any point, and
let 0 be the angle made by the bar with the axis of symmetry: then

T- 1

^-~~dr ^-~fdO’

also let the section of the bar be

a = dy dz

and let the axis of the bar pass through the origin from which we have
developed the potential in terms of spherical harmonics. Wo can then
write as before

r=A,Q,r+A,,, +A,Q,r>+ etc.

where Q„ Q,),, etc., are zonal spherical harmonics with reference to
the angle 6,

from which we have the following:

X* = A‘Q> + 9A*,,Q‘,y + ZSAiQlr' + 6A,A,„Q,Q„/*

+ 10A,ArQ,Qrr* + dOA,j^A,Q,„Q,r‘ + etc.,

F* = {A^,Q'> + + A^Q'y + %A,AM\,!<^

H- ^^A.AyQ'Q'rT* iiA„,AyQ',,,Q'yr* + etc.} sitt’^»

XF= -{A‘(3,e: + -f BAlQyO'yr* -F (3<2;<?,„

+ + mQr + Q,Q'r)A,A,1* -I- (6Q'„,Qy

+ ‘^Qin^r) A,„AyiA + etc } sin

The moment of the force tending to increase is

whence we may write,

B = — \a\A{(JCy — Tc^ a* + i,) -l- — i,) a'’ — 0 (ki — a«'},

190

Henry A. EowiiANd

' ^ '^'^■

where Z is half the length of the bar and [i = cos 6.

A=UBmO\A^,Q^Q', + + ^A\Q.Q'^> + A,AMQ,„

+ QM P + A4, (Q’Q, + Q^Q',) 1* + i^A„,A, (Q',,,Q, + Q,„ Q',)l^]
B =U Bin 0{ A‘ {q^Qf; 8ia“ e - <?;» cos 0) + AJ,, sin* 0

- 0:^ COB 0)-L + Ar (Q'yQ'J sin* 0 - Q', cos 0) + A,A,„

+ C7c;j cos <») -|- + a, a, m.Q" + q'iq^) o

-2«:c; costf) |. + A, c>'/ + c>"a>o 8in*^>

-^Q'^j>Qr eoso)^'^,

0= + U { A5 + Q';) sin’ - e><?: cos 0 ) + tiA], {{QM,

+ <2« ) Bin*tf- cos ^ + 6^1* - V?) Siu*^;

- G,<2; 008 <?)-|- +A^,,,(i^Q\Q\,^+ 8in*<?

- + Q£t’„^ cos 0) I + A, Ay i(r)Q',Q'y + 5</;gy + q'^q!,

+ Q^Qy) sin* 0 - (^SQ'^Q, + Q^Q',) cos 0) • J + A,,, Ay ((S(>"/^,

+ + BQ[,,Q'y + sin* 0 — (S

+ ^QtiiQ'y) cos e) j..

Where

Qj =COB0,

Qtu = i (5 cos’ o — z cos 0) ,

Qy =i (63 cos* — 70 cos * 0 + If) cos o) ,

e: =1,

e:,, =1(5 cos* .7-1),

Q'y = Y-(^lcos*(i'— 14cOB’tf + 1),

Q7 =0,

Q7„ = 16 cos 0,

Q'y' = ■¥ (^1 cos’ (l — H cos II) ,
fi =Qoa 9.

Diamagnbtio Constants ot Bibmoth and Oalo-Spas 191

A = il6in0\ + |.J A'J* + JjVjf AM> — A,AJ^

- H- „?

- /*“ +

+ i\i.A,Ayl^ - ^1,9.1 A„, A J*) /.» + (- Ji-^- + AJi ^„^v2*) /x"

+ UigijaAj»ivh

5 = 4Z sin 0 { (- A^ - fj - 3^^^AU‘ + 6A,A,,/ - i^.A^,1^

+ ^A^.AJ^) /X + (&i.A]J-m&.AJ>-10A,A,J+^LA,A,V

-^lS.A,„Ajr)^’‘ + (_A|Ayi5^/

O' = 4H(- + ^A^AJ^-jiA,,^^)

+ (-1 J^„/) /X + (- W J* -

+ /x» + 9J,xl„;v* + i^A'J +

+ ^ A^J^ + Aji A,A,1^ - A.J|A A ,,,AJ‘) /X* - yi A,A,,/m’

+ (- Ji^l A‘J* - x.y>^U - l|t A^AyP + A,,^yl‘) /X*

+ ^'vf - ^Arl‘) /•*'}•

Or we can write

s=! 4Z sin I Lit. + iV+ X"/x‘ + etc. },
if = 4i sin I Mil. + M'ti* + etc. },

0 = aZ { JV + JVV + N"A + etc. \,

where the values of L, M, etc., are apparent.

To sum up wo may then write as before

9= -ia{ A [(*. - *0 a* + A,1 + B [(/fc. - k,) «'• + *,] - a {k, - h ) ««' }

where A, B and 0 are the quantities we have found, a is the cosine of
the angle made by the axis of the crystal with the axis of the bar, and a'
is the cosine of the angle made by the same axis with a horizontal line
at right angles to the bar.

The equation

9 = 0

gives equilibrium at some angle depending on « and a', and if either of
these is zero the angle can be cither <f = 0 or iz, one of which will be
stable and the other unstable according as the body is para- or dia-
magnetic.

Tor a diamagnetic crystal like bismuth with the axis at right angles
to the bar we can put

II = cos 0 = sin tf' and a = 0 ,

and we can write

19^

Henet a. Eowland

6 = ^ \ a{ {Lii + Lij!^ + etc.)

4" 4Z [(^1 — ^a) o!^ + lc^\_iffx 4- M.* 4" etc.] }

or for very small values of /« we can write in terms of <p

^ = - aaZ0 {Tc^L 4- {(Jk^ - h) «'* + h) M\.

If I is the moment of inertia of the bar and t is the time of a single
vibration, we may write

If we hang up the har so that o' = 0 we have

Jc,(^L + M) = -

and if we hang it up so that a! = iK we have again

whence

where

h =
h =

L-r M.'

i = a; - 4- 4- ^A\P

M= - A] + ^ i* 4-

L + M= SA^AJ^ - + ^-A,A^)t^ 4 -

For a cleavage bar of calc spar we must use the general equation.
For equilibrium we have

Jci\Aa^ 4- — C7aa'} 4- h^\A (1 — tt*) 4- E (1 •— </®) 4" Oaa ^ } = 0,

which gives us the ratio of fcj to For this experiment it is best to
hang up the bar so that the axis is in the horizontal plane and we
should then have

a’* = 1 — a!\

For obtaining, another relation it is best to suspend the bar with «' = 0
and we then have the position of stable equilibrium at the point ^/ = Jtt
which gives

(9 = — %al4> { L [(ii - /fca) a» + *,] +Mh)=. 4' ,

whence

DiAMAaiTETio Constants of Bismttth and Caio-Spae 193

these various eq^uatious give the complete solution of the proUem of
finding the various coefficients of magnetization.

Part II. — By W. W. Jacqvbb

In the foregoing part of this paper there have been deduced mathe-
matical expressions for the constants ft and h' both for bismuth and
for calc-spar crystals. In these expressions it is necessary to substitute
certain quantities obtained by a series of experiments, and it is the
purpose of the remaining portion of the paper to describe briefly the
way in which these quantities were obtained. *

These experiments are naturally divided into two parts. Krst, the
exploration of the small magnetic field between the two poles of the
electromagnet, and second, the determination of the time of swing and
certain other constants relating to little bars of the substances experi-
mented upon when suspended in this field.

In order to insure the constancy of the magnetic field, a galvano-
meter and variablo resistance were inserted in the circuit through
which the magnetizing current circulated. This space between the
poles of the electromagnet in which the experiments were performed
was a little larger than a hen’s egg.

The method of exploring this field was as follows: In the line join-
ing the centre of the two iiolcs was placed a little brass rod, along
which a very small coil of fine wire was made to slide. To this rod
were fixed two little set-screws to regulate the distance through which
the coil could be moved. Starting now always from the centre, the
coil was moved successively through distances a, i and e, and the cor-
responding deflections of a delicate mirror galvanometer contained in
the circuit were noted. To each of these deflections was added the
deflection due to quickly pulling the coil away from the centre to a
distance such that the magnetic potential was negligibly small. Of
course, experiments were made on botli sides of the centre of the field
in order to eliminate any want of symmetry, and the distances through
which the coil moved were all carefully measured with a dividing engine.

In order to reduce the deflections of the galvanometer to absolute
18

194

HbNET a. EoWIiA-KD

measure, an earth inductor was included in the circuit with the little
coil and galvanometer and the deflections produced by this were com-
pared with those produced by moving the little coil. These deflections
were taken between every two observations with the little coil.

The deflections due to moving the little coil, those due to the earth
inductor and that due to pulling the coil away from the centre are
given in the folio-wing table:

Distance a. Distance h. Distance c.

Coil 4-407 cm. 9-666 cm. 6-363 cm.

Earth inductor 33-138 cm. 33-137 cm. 33-162 cm.

Drawing coil away from centre 67*416 cm.

In order to determine the propCT quantities for substitution in the
expression for the magnetic potential of the field, it was necessary to
measure, besides, the deflections due to the little coil when moved
through various distences and those due to the earth inductor.

The mean radius of the small coil = -3912 cm.

Number of turns =83-

Width if coil = *1824 cm.

Depth of coil = -1212 cm.

Integral area of earth inductor = 20716-2 cm.

Horizontal intensity of earth^s magnetism = -1984 cgs.

The quotient of the mean radius of the coil by the distance moved
gave tan 6 .

The linear measurements were made with a dividing engine.

The horizontal intensity of the earth^s magnetism was determined
by measuring the time of swing of a bar magnet and its effect upon a
smaller galvanometer needle. The proper substitution of these quan-
tities in the formula given gave the expression in absolute measure
for the magnetic potential at any part of the field.

The remaining part of the experiment and the part that was attended
with greatest difficulty, was to prepare little bars of the substances and
to determine the times of vibration of these when suspended, first with
the axis vertical and then with it horizontal in the magnetic field.
Besides this, the dimensions and the moment of inertia of each bar had
to be determined, and, in the ease of the calc-spar, the angle the bar
made with the equatorial line of the poles when in its position of equi-
librium, had to be measured.

Bismuth and calc-spar were the two crystals experimented upon;
quite a number of other substances were tried but failed to give good

Diamagnetic Constants ot BisMTn?H and Calo-Spae 195

Tssults l)6c&xis6 of the ixoE coDtsinsd in tlienx as ad impuiity. Th.6
bArs were OAch About 16 mm. long and About 8 mm. in cross section.
The force to be measured being only about -00000001 of that exerted in
the case of iron it was necessary to carry out the experiments urith the
very greatest care.

In order to obtain bars free from iron, very fine crystals of chomicaUy
pure substances were selected and the bars cleaved from them. They
were then polished with their various sides parallel to the cleavage
planes by rubbing on clean plates of steatite with oil. In order to
remove any particles of iron that might have coUected upon them
during these processes, they were carefully washed with boiling hydro-
chloric acid and with distilled water and then wrapped in clean papers,
and never touched except after washing the hands with hydrochloric
acid and distilled water.

In order to reduce to a minimum the causes that might interfere
with the accurate determination of the times of vibration of these bars
the poles of the magnet were encased by a box of glass. From the top
of this a tube four feet long extended up toward the ceiling, and
this was hung a single fibre of silk so small as to be barely visible to
the naked eye. The bars were placed in little slings of coarser silk
fibre and suspended by this. Outside the glass case was a microscope
placed horizontally and having a focus of about six inches. This was
directed toward the suspended bar, and when the latter was at rest the
cross hairs of the microscope fell upon a little scratch in one end of the
bar. Near by was a telegraph sounder arranged to tick seconds. The
bar was set swinging through a small arc by making and breaking the
current, and the interval between two successive transits of the little
scratch on the bar by the cross hairs of the microscope was measured
in seconds and tenths of a second by the car. By keeping count through
a largo number of successive transits the time of a single swing could
be determined with very great accuracy. The bar was oaused to swing
only through a few degrees of arc and such small correction for ampli-
tude as was found necessary was applied. The time of swing was deter-
mined first with the axis vertical and then with it horizontal. But
besides the time of swing of each bar it was necessary to measure: the
length; area of section; moment of inertia in each position; and for the
calc-spar bar the angle it made with the ecjuatorial plane of the magnet
when in its position- of equilibrium. This was not necessary in the
case of bismuth, because its position of equilibrium lay in the equatorial
plane.

196

Hbnbt a. Rowlaot>

Axis, vertical ...
Axis, horizontal

BlSUUIH.

Time of Moment of

swing. inertia.

7*18 sec. -10976 cgs.
5-76 sec. -10943 cgs.

Oalc-Spab.

Half Area of

length. section.

•7709 cm. -03778 cm.

Time of Homent of Half Area of
swing. Inertia. length. section.

Axis, vertical ...
Axis, horizontal

46-33 sec. -0303 cgs.
43-39 sec. -0300 cgs.

*8016 cm.

•0800 cm. 60® 30'

The iiTiAftr measurements were made with a dividing engine, the
moments of inertia were calculated from the dimensions of the bars.
The angle at which the calc-spar stood was measured by projecting the
linear axis on a scale placed at a distance.

The above quantities being all determined and properly substituted,
the solution of the equations gave for

Bismuth -000 000 013 554

— -000 000 014 334

Calc-spar — -000 000 037 930

= — -000 000 040 330

PRELIMIITAEY NOTES ON MR. HALL’S RECENT DISCOVERY"

[Philottophieal [6], JX, 482-484, 1880 ; ProcMdings of the Physical Sodcty^ IT,

10-18, 1880; American Journal of Mathematics, XT, 854-856, 1879]

The recent discovery by Mr. Hall ’ of a new action of magiretism on.
electric currents opens a wide field for the mathematician, seeing that
we must now regard most of the equations which we have hitherto used
in electromagnetism as only appro:simate, and as applying only to some
ideal substance which may. or may not exist in nature, but which cer-
tainly docs not include the ordinary metals. But as the effect is very
small, probably it will always be treated as a correction to the ordinary
equations.

The facts of the case seem to be as follows, as nearly as they have
yet been determined: — ^Whenever a substance transmitting an electric
current is placed in a magnetic field, besides the ordinary electromotive
force in the medium, we now have another acting at right angles to the
current and to the magnetic lines of force. Whether tiiere may not be
also an electromotive force in the direction of the current has not yet
been determined with accuracy; but it has been proved, within the limits
of accuracy of the experiment, that no electromotive force exists in the
direction of the lines of magnetic force. This electromotive force in a
given medium is proportional to the strength of the current and to
the magnetic intensity, and is reversed when either the primary current
or the magnetism is reversed. It has also been lately found that the
direction is different in iron from what it is in gold or silver.

To analyse the phenomenon in gold, let us suppose that the lino A B
represents the original current at the point A, and that BC is the now
effect. The magnetic pole is supposed to be either above or below the
paper, as the case may be. The line A 0 will represent the final
resultant electromotive force at the point A. The circle with arrow
represents the direction in which the current is rotated by the mag-
netism.

1 From the American Journal of Mathematics. Communicated by the Physical
Society.

a Phil. Ma{?. [5], vol. lx, p. 226.

198

HeNET, a. EoWItAND

It is seen that all these effects are such as would happen were the
electric current to be rotated in a fixed direction with respect to the
lines of magnetic force, and to an amount depending only on the mag-
netic force and not on the current. This fact seems to point imme-
diately to that other very important case of rotation, namely the rota-
tion of the plane of polarization of light. For, by Maxwell’s theory,
light is an electrical phenomenon, and consists of waves of electrical
displacement, the currents of displacement being at right angles to the
direction of propagation of the light. If the action we are now con-
sidering takes place in dielectrics, which point Mr. Hall is now investi-
gating, the rotation of the plane of polarization of light is explained.

I give the following very imperfect theory at this stage of the paper^
hoping to finally give a more perfect one either in this paper or a
later one.

Korth Pole above.

Let $ be the intensiiy of the magnetic field, and let J? bo the original
electromotiTe force at any point, and let c be a constant for the given
medimn. Then the new electromotive force E' will bo

E' = t^E,

and the £nal electromotive force will be rotated through an angle which
will be very nearly equal to c$. As the wave progresses through the
medium, each time it (the electromotive force) is reversed it will be
rotated through this angle; so that the total rotation will be this quan-
tity multiplied by the number of waves. If A is the wave-length in air,
and i is the index of refraction, and o is the length of medium, then

the number of waves will be j, and the total rotation

0=ct^i.

The direction of rotation is the same in diamagnetic and ferromag-
netic bodies as we find by experiment, being different in the two; for it

Pbbliminaet Notes on Ms. Hall’s Bboent Disoovebt 199

is well known that the rotation of the plane of polarization is opposite
in the two media, and Mr. Hall now finds his effect to be opposite in
the two media. This result I anticipated from this theory of the
magnetic rotation of light.

But the formula makes the rotation inversely proportional to the
wave-length, whereas we find it more nearly as the square or cube.
This I consider to be a defect due to the imperfect theory; and it would
possibly disappear from the complete dynamical theory. But the for-
mula at least makes the rotation increase as the wave-length decreases,
which is according to experiment. Should an exact formula be finally
obtained, it seems to me that it would constitute a very important link
in the proof of Maxwell’s theory of light, and, together with a very
exact measure of the ratio of the electromagnetic to the electrostatic
units of electricity which we made here last year, will raise the theory
almost to a demonstrated fact. The determination of the ratio will
be published shortly; but I may say here that the final result will not
vary much, when all the corrections have been applied, from 999,'>'00,000
metres per second; and this is almost exactly the velocity of light. We
cannot W lament that the great author of this modem theory of light
is not now hero to work up this new confirmation of his theory, and
that it is left for so much weaker hands.

But before we can say definitely that this action explains the rotar
tion of the plane of polarization of light, the action must be extended
to dielectrics, and it must be proved that the lines of electrostatic
action arc rotated around the lines of force as well as the electric cur-
rents. Mr. Hall is about to try an experiment of this nature.

I am now writing the fiall mathematical theory of the new action, and
hope to there consider the full consequences of the new discovery.

Addition . — have now worked out the complete theory of the rota-
tion of the plane of polarization of light, on the assumption that the
displacement currents are rotated as well as the conducted currents.
The result is very satisfactory, and makes the rotation proportional to

4*5

, which agrees very perfectly with observation. The amount of rota-
tion calculated for gold is also very nearly what is found in some of
the substances which rotate the light the least. Hence it seems to me
that we have very strong ground for supposing the two phenomena to
be the same.

ON THE BFFICIINCT OF EDISON’S ELECTEIC LIGHT

Br H. A. Rowland and Gbobge F. Babkbb
I American Jowrnal of Science^ [8], XTX, 887-889, 1880]

The great interest which is now being felt throughout the civilized
world in the success of the various attempts to light houses by elec-
tricity, together with the contradictory statements made with respect
to Mr. Edison^s method, have induced us to attempt a brief examina-
tion of the eflSieiency of his light. We deemed this the more important
because most of the information on the subject has not been given to
the public in a trustworthy form. We have endeavored to make a
brief but conclusive test of the efficiency of the light, that is, the
amount of light which could be obtained from one horse power of work
given out by the steam engine. For if the light be economical, the
minor points, such as making the carbon strips last, can undoubtedly
be put into practical shape. ‘

Three methods of testing the efiSlciency presented themselves to us.
The first was by means of measuring the horse power required to drive
the machine, together with the number of lights which it would give.
But the dynamometer was not in very wood working order, and it was
difficult to determine the number of lights and their photometric
power, as they were scattered throughout a long distance, and so this
method was abandoned. Another method was by measuring the resist-
ance of, and amount of, current passing through a single lamp. But
the instruments available for this purpose were very rough, and so
this method was abandoned for the third one. This method consisted
in putting the lamp under water and observing the total amount of heat
generated in the water per minute. For this purpose, a calorimeter,
holding about kil. of water, was made out of very thin copper : the
lamp was held firmly in the centre, so that a stirrer could work around
it. The temperature was noted on a delicate Baudin thermometer
graduated to 0-1° C.

As the experiment was only meant to give a rough idea of the
efficiency within two or three per cent, no correction was made for

On the Epmoiency op Edison's Blectrio Light

301

radiation, but the error was avoided as much as possible by having the
mean temperature of the calorimeter as near that of the air as possible,
and the rise of temperature small. The error would then be much less
than one per cent. A small portion of the light escaped through the
apertures in the cover, but the amount of energy must have been very
minute.

In order to obtain the amount of light and eliminate all changes of
the engine and machine, two lamps of nearly equal power were gener-
ally used, one being in the calorimeter while the other was being
measured. They were then reversed and the mean of the results taken.
The apparatus for measuring the light was one of the ordinary Bunsen
instruments used for determining gas-lights, with a single candle at
ten inches distance. The candles used were the ordinary standards,
burning 120 grains per hour. They were weighed before and after
each experiment, but as the amount burned did not vary more than
one per cent from 130 grains per hour, no correction was made.

As the strips of carbonized paper were flat, very much more light
was given out in a direction perpendicular to the surface than in the
plane of the edge. Two observations were taken of the photometric
power, one in a direction perpendicular to the paper, and the other
in the direction of the edge, and we are required to obtain the average
light from these. If L is the photometric power perpendicular to the
paper, and I that of the edge, then the average, ^ will evidently be
very nearly

J f^O /•o

' cos a sin a rf « -j- ? / sin*-* a d a.

n/irr

In the paper lamps vre found l = nearly; henee X=%L nearly.
The lamps nsecl wore as follows:

No.

Kind of Carbon.

Slisoof Carbon.

Approximate
roslstanoe whoa cold.

6R0

Paper.

Lar^o.

147 ohmB.

301

((

147 “

850

Small.

170 «

809

154 “

817

Fibre.

Lari^e.

87 “

The capacity of the calorimeter was obtained, by adding to the capac-
ity of the water, the copper of the calorimeter and the glass of the

202

Hbnet a. Eowland

lamp and thermometer. The calorimeter and cover weighed 0*103
Ml. and the lamps about 0*035 Ml.

First experiment, Ifo. 201 in calorimeter and No. 580 in photometer;
capacity of calorimeter = 1*153 -j- *009 + •007' = 1*169 kil. The
temperature rose from 18® *28 0. to 23® *11 C. in five minutes, or 1®*75
F. in one minute. Taking the mechanical equivalent as 775*, which is
about right for the degrees of this thermometer, this corresponds to
an expenditure of 3486 foot pounds per minute. The photometric
power of No. 580 was 17*5 candles maximum, or 13*1 mean, X.

When the lamps were reversed, the result was 3540 foot pounds for
No. 580, and a power of 13*5 or 10*1 candles mean. The mean of
these two gives, therefore, a power of 3513 foot pounds per minute for
11*6 candles, or 109*0 candles to the horse power.

To test the change of efficiency when the temperature varied, we
tried another experiment with the same pair of lamps, and also used
some others where the radiating area was smaller, and, consequently,
the temperature had to be higher to give out an equal light.

We combine the results in the following table, having calculated the
number of candles per indicated horse power by taking 70 per cent of
the calculated value, thus allowing about 30 per cent for the friction
of the engine, and the loss of energy in the magneto-electric machine,
heating of wires, etc. As Mr. Edison^s machine is undoubtedly one of
the most efficient now made, it is believed that this estimate will be
found practically correct. The experiment on No. 817 was made by
observing the photometric power before and after the calorimeter
experiment, as two equal lamps could not be found. As the fibre was
round, it gave a nearly equal light in aU directions as was found by
experiment.

Lam]^

sused

Photometric Power.

Capacity of Cal-
orimeter In Ihs.

Bise of tempera-
ture In decrees
P.

Energy per min-!
nte In root-lbs. [

Mean number of;
candles per;
horse power of
electrloity.

Mean number of
gas jets of 16.
candles each
perhorse power !
of electricity. =

Mean number of
gas jets per In^ !
dicated horse i
power. j

Csdori-

metor.

Photo-

meter.

Measured
perpen-
dloular to
paper, L.

Average,

201

580

17-5

IS-l

2-57

1®*75

3486*

580

201

18-5

10-1

2,82

l®-62

3540-

j- 109*0

6*8

4*8

580

201

38*5

28-9

3.74

2° -44

5181-

201

580

44-6

88-5

2 76

3" -39

4898-

j- 304 8

13*8

8*9

850

809

190

14-3

3.81

1®-14

2483-

809

850

12-2

9*2

3.79

l®-54

8880-

J. 138*4

8*8

5*8

817

17-2

2.73

1»*28

2708*

309*6

18*1

9*3

On the EPEioiENoy op Edison’s Eleothio Light

203

The increased efficiency, with rise of temperature, is clearly shown
by the table, and there is no reason, provided the carbons can be made
to stand, why the number of candles per horse power might not be
greatly increased, seeing that the amount which can be obtained from
the arc is from 1000 to 1500 candles per horse power. Provided the
lamp can be made either cheap enough or durable enough, there is no
reasonable doubt of the practical success of the light, but this point
will evidently reqxnre much further experiment before the light can be
pronounced practicable.

In conclusion, we must thank Mr. Edison for placing his entire
establishment at our disposal in order that we might form a just and
unbiased estimate of the economy of his light.

ELECTRIC ABSORPTION OF CRYSTALS

By H. a. Rowland and E. L. Nichols *

[Philosophical Magazine [6], XJ, 414-419, 1881; Pt'oceedings of the Physical Society^ /V,

215-221, 1881]

The theory of electric ahsorption does not seem to have as yet
attracted the general attention which its importance demands; and
from the writings of many physicists we should gather the impression
that the subject is not thoroughly understood. Ifevertheless the sub-
ject has been reduced to mathematics; and a more or less complete
theory of it has been in existence for many years. Clausius seems to
have been the first to give what is now considered the best theory.
His memoir, ^ On the Mechanical Equivalent of an Electric Discharge,^
&c., was read at the Berlin Academy in 185^.“ In an addition to this
memoir in 1866 he shows that a dielectric medium having in its mass
particles imperfectly conducting would have the property of electric
absorption. Maxwell, in his ^Electricity,’ art. 325, gives this theory
in a somewhat different form, and shows that a body composed of layers
of different substances would possess the property in question. One
of us, in a note in the ^American Journal of Mathematics,’ ITo. 1,
1878, put the matter in a somewhat different form, and investigated
the conditions for there being no electric absorption.

All these theories agree in showing that there should be no electric
absorption in a perfectly homogeneous medium. A mass of glass can
hardly be regarded as homogeneous, seeing that when wo keep it
melted for a long time a portion separates out in crystals. Glass
can thus be roughly regarded as a mass of crystals with their axes in
different directions in a medium of a -different nature. It should
thus have electric absorption. Among all solid bodies, wo can select

1 Comnmiiicated by the Physical Society, having been read May 14th, 1881.

2 1 have obtained my knowledge of this memoir from the French translation, en.
titled Thiorie Mhanique de la Chaleur, par R. Clansins, translated into French by F.
Folie: Paris, 1869. The ^Addition^ does not appear in the memoir published in
Pogg. Ann., vol. Ixxxvi, p. 887, hut was added in 1866 to the collection of memoirs.

Electric Absorption op Crystals

205

none which we can regard as perfectly homogeneous along any given
line through them, except crystals. The theory would then indicate
that crystals should have no electric absorption; and it is the object of
this paper to test this point. The theory of both Clausius and Max-
well refers only to the case of a condenser made of two parallel planes.
In the ^Wote^ referred to, one of us has shown that in other forms
of condenser there can be electric absorption even in the case of homo-
geneous bodies. Hence the problem was to test the electric absorp-
tion of a crystal, in the case of an infinite plate of crystal with parallel
sides. The considerations with regard to the infinite plate were
avoided by using the guard-ring principle of Thomson.

The crystals which could be obtained in large and perfect plates
were quartz and calcite. These were of a rather irregular form, about
35 millim. across and* millim. thick, and perfectly ground to plane
parallel faces. There were two quartz plates cut from the same crystal
perpendicular to the axis, and two cleavage-plates of Iceland spar.
There were also several specimens of glass ground to the same thickness;
the plates were all perfectly transparent, with polished faces. Exam-
ined by polarized light, the quartz plates seemed perfectly homo-
geneous at all points except near the edge of one of them. This one
showed traces of amethystine structure at that point; and a portion
of one edge had a piece of quartz of opposite rotation set in; but the
portion which was used in the experiment was apparently perfectly
regular in structure. The fact that there are two species of quartz,
right- and left-handed, with only a slight change in their crystalline
structure, and that, as in amethyst, they often occur together, makes
it not improbable that most pieces of right-handed quartz contain
some molecules of left-handed quartz, and vice versa. In this case
quartz might possess the property of electric absorption to some
degree. But Iceland spar should evidently more nearly satisfy the
conditions. It is unfortunate that the two pieces of quartz were not
cut from different crystals.

This reasoning was confirmed by the experiments, which showed
that the quartz had about one-ninth the absorption of glass; but that
the Iceland spar had none whatever, and is thus the first solid so far
found having no electric absorption. Some crystals of mica, &c., were
tried; but calc spar is the only one which we can say, d priori, is per-

» [There is a gap Id the printed article. On examination of the various plates if
the Physical Laboratory of the Johns Hopkins University, some have been found on
about 2 mm. thickness, which are probably those used in this research.]

306

Hsumy A. Eowlaito

fectly homogeneous. Thus mica and selenite are so very lamellar in
their character, that fev specimens ever appear in which the In-Tninm
are not more or less separated from one another; and thus they should
have electric absorption.

In the ordinary method of experimenting with the various forms of
Leyden jar, there are, besides the residual discharge due to electric
absorption in the substance of the insulator, two other sources of a
return charge. The surface of the glass being more or less conduct-
ing, an electric charge creeps over the surface from the edges of the
tinfoil. In discharging the jar in the usual way by a connecting wire,
this surface remains charged, and the electricity is gradually con-
ducted back to the coatings, and thus recharges them. If, fmrther-
more, the coatings be fastened to the glass with shellac or other cement,
the return chafge may be partly due to it; for we have between the
coatings not merely glass, but layers of glass, cement, &e., which the
theory shows to give a residual discharge. Besides the coatings are
not planes; and hence, as one of us has shown, there may be a return
charge, even if the glass gave none between infinite planes. If the
plates were merely laid on the glass without cementing, the same
result would follow, since the insulator would then consist of air and
glass in layers.

In the present research these were sources of error to be avoided,
since the residual discharge due to the insulating plates themselves
were to be compared. The condenser-plates were copper disks. Those
were amalgamated, so that there was a layer of mercury between them
and the dielectric, which excluded the air and conducted the electricity
directly to the surface of the dielectric: thus the condition of a single
substance between the plates was fulfilled. The errors dxro to the
creeping of the charge over the surface of the dielectric and that due
to the plates not being infinite were avoided, the first entirely and the
second partially, by the use of the guard-ring principle of Sir Wm.
Thomson.

Plate IV represents this apparatus. The plate of crystal, e, was
placed between two amalgamated plates of copper, a and 6, over the
upper one of which the guard-ring, d, was carefully fitted; this ring,
when down, served to charge and discharge the surface around the
plate, a; and so the errors above referred to from the creeping of the
charge along the plate, and from the plate not being infinite, were
avoided.

308

Henry A. Eowland

The charging battery consisted of six large Leyden jars of nearly a
square foot of coated surface each, charged to a small potential.
Although accurate instruments were at hand for measuring the poten-
tial in absolute measure, it was considered sufficient to use a Harris
xmit-jar for giving a definite charge; for very accurate measurements
were not desired, and the Harris unit- jar was entirely sufficient for the
purpose. The return charge was measured by a Thomson quadrant-
electrometer of the original well-known form.

The apparatus shown in Plate IV performs all the necessary opera-
tions by a half turn of the handle By two half turns of the handle,
one forward and the other back, the crystal condenser could be succes-
sively charged from the Leyden battery, discharged, the guard-ring
raised, the upper plate, a, again insulated, and the connection made
with the quadrant-electrometer.

The copper ring, d, was suspended by three silk threads from the
brass disk, f, which in turn could be raised and lowered by the crank, //.
A small wire connected the ring with the rod on which was the ball, li.
This rod was insulated by the glass tube i, and could revolve about an
axis at fc. By the up-and-down motion of the rod the ball came into
contact with the ball (Z) connected with the earth, or the ball {rri) con-
nected with the battery. When the cranks were in the position shown
in the figure, the heavy ball n caused the ball to rise and press
against Z; but when f descended, the piece o pressed on the rod and
caused % to fall on m.

Another rod, q, also more than balanced by a ball, r, was insulated by
a glass tube, a, and connected with the quadrant-electrometer by a
very fine wire. It could also turn around a pivot at t; so that when
the ring u rested upon it, it fell on the upper condenser-platc a, and
connected with the electrometer; when the weight u was raised by the
crank v, the rod rested against /, and so connected tho electrometer to
the earth, to which the other quadrants were already connected.

At the beginning of an experiment, the insulating plate to be tested
having been placed between the condenser-plates a and 6, the handle
was brought into such a position that the ring, d, rested on the plate
around a. The lengths of the threads between d and f were such that o
for this position of the handle did not touch w, and so h remained in
connection with the earth; and so d was also connected with tho earth,
and thus also with b. On now turning the handle further, the hall h
descended to the ball m, and thus charged the condenser for any time
desired. On now reversing the motion, the following operations took
place :

Bleoteio Absobption op Cbtstals

209

First, the ball h rose and discharged the condenser.

Second, the gnard-ring d ascended.

Third, the rod g, •which had been previonsly ia contact •with p, thus
bringing the qnadrant-clectrometer to zero, now moved do^wn and rested
on the upper condenser-plate a. Thus any return charge quickly showed
itself on the electrometer. The amount of deflection of •the instru-
ment depends upon the character of the dielectric, its thickness, the
charge of the battery, the time of contact -with the battery, and upon
the length of time of discharging.

In comparing the glass •with the crystal plates, the electrometer was
rendered as little sensitive as the or^nary arrangement of the instru-
ment •without the inductor-plate would allow. The electric absorp^tion
of the glass plates for a charge in the battery of two ox three sparks
from the Harris unit-jar then sufficed, after 20 or 30 seconds contact
with the battery and 5 seconds discharging time, to give a deflection of
about 200 scale-divisions, which were millimetres. The quartz and
calcite plates were then alternately substituted for the glass, the same
charge and the same intervale of contact being used, and the resulting
deflections noted — two plates of each substance of the same thickness
being used.

The results of the measurements are given in the following Tables,
the effect of the glass being called 100.

TABLE I.

( 0 )

April 13, 1880.

Charge of battery, % aparks.
Contact, 80 aeconda.

Glaas (lat plate) 100-0

Quartz (iat plate) 17-1

(2nd plate) 90-0

Calcite (1st plate) 0.0

C3nd plate) 0-0

( 6 )

April 18, 1880.

Charge of battery, 8 sparks.
Contact, 20 seconds.

Glass (let plate) 100-0

Quartz (1st plate) 19 -B

Calcite (1st plate) 0-0

(cl

April 14, 1880.

Charge, 8 sparks.

Contact, 10 seconds.

Plates carefully dried by being in desic-
cator over night.

Glass (1st plate) 100-0

Quartz (1st plate) 10-7

Calcite (1 st plate) 0-0

(d)

April 29, 1880.

Charge, 2 sparks.
Contact, 80 seconds.

Plate in desiccator since April 14.

Glass (2nd plate) 100-0

** (1st plate) 90-8

Quartz (1st plate) 18*4

** (9nd plate) 12*1

Calcite (1st plate) 0i>0

“ (2nd plate) 0-0

210

Hbnbt a. E 0 WI 1 A.ND

TABLE 11.

Mat 1. — Bblativh Ebfbotb bob Dibbbrbnt Intbnsitibs ob Chabok and
Timb ob Contact

.Oharffe of
Battery.

Material.

Defleotlons, in millimetres.

Contact,

5 seconds.

Contact,

10 seconds.

Contact,

20 seconds.

Glass (Ist)

188-0

189-8

225*0

One spark . . . <

Quartz (Ist) . . ,

18-0

22-7

84-8

Calcite (Ist)...

0-0

Glass (let)

Off the scale

Two sparks. . <

Quartz (Ist). . .

24-0

86-0

50-0

Calcite (let). . .

0-0

These Tables seem to prove beyond question that calcite in clear
crystal has no electric absorption. Quartz seems to have about that of
glass; but we have remarked that quartz is not a good substance to test
the theory upon.

Some experiments were made with cleavage-plates of selenite, which
are always more or less imperfect, as the lamina? are very apt to sepa-
rate. These gave, however, eflEects about -J or i those of glass.

In order to test still further the absence of electric absorption in
calcite, the electrometer was rendered very sensitive, and the calcite
plates were tested with gradually increasing charges, from that which
in glass gave 200 millim. after 1 second contact, up to the nuiximuin
charge (ten sparks of the unit-jar) which the coiKlonscrs wore capable
of carrying. In these trials, the calcite still showed no effottt, oven
with 30 seconds contact. During these experiments glass was fre-
quently substituted for the calcite, to leave no question but that the
apparatus was in working order.

It is to he noted that the relative effects of the quartz and tlio glass
were different for dried plates and plates exposed to the alinosi)horo.
This was possibly due to the glass being a better insulator, nn<l thus
retaining its charge better when dry than in its ordinary condition.

Thus we have found, for the first time, a solid which has no electric
absorption; and it is a body which, above all others, the theory of
Clausius and Maxwell would indicate. The small amount of the effect

Eleoteio Absobption OS' Crystals

811

in quartz and selenite also confirms the theory, provided that we can
show that in the given piece of quartz some molecules of right-handed
quartz were mixed with the left; for we know that the theoretical con-
ditions for the absence of electric absorption are rarely satisfied by
laminated substances like selenite or mica. If the theory is con-
firmed, the apparatus here described should give the only test we yet
have of the perfect homogeneity of insulating bodies; for any optical
test cannot penetrate, as this does, to the very structure of the
molecule.

OF ATMOSPHEEIC ELECTEICITY

[Presented to the Congress of Electricians, Paris, September 17, 1881, and here
translated from their Proceedings]

IJohm Eopkim XTniversity Circvlariy No. 19, pp. 4, 5, 1883]

Among the subjects to be discussed by this Congress is that of atmos-
pheric electricity, and I should like, at this point, to urge the import-
ance of a series of general and accurate experiments performed simul-
taneously on a portion of the earth^s surface as extended as possible.
Here and there on the globe, it is true, an observer has occasionally
performed a series of experiments, extending even over several years:
but the different observers have not worked in accordance with any pre-
concerted plan, it has not been possible to compare their instruments,
and even where absolute measurements have been obtained, the exact
meaning of the quantity measured has not been perceived. Let us
take, for instance. Sir William Thomson's water dropping apparatus,
which is used at the Kew Observatory. This apparatus is composed
of one tube rising a few feet above the building and of anotlier tube
near the ground, so that it is in the angle made by the house and th(^
ground. This apparatus indicates a daily variation in the electricity
of the atmosphere, but the result is evidently influenced by the condi-
tions of the experiment. Another observer who should fit up an appar-
atus in another country might obtain entirely different conditions, so
that it would be impossible to compare the results. Hence the noc(‘8-
sity of having a system.

The principal aim of scientific investigation is to be able to under-
stand more completely the laws of nature, and we generally succ(‘od in
doing this by bringing together observation and theory. In science
proper, observations and experiments are valuable only in so far as they
rest on a theory either in the present or in the future. We can as yet
present only a plausible theory of atmospheric electricity, but tluj real
way of arriving at the truth in this case is to let ourselves be guided in
our future experiments by those which have hitherto been made on
this subject.

On Atmosphbbio Elbotrioity

213

The principal facts which have been discovered can be stated in a few
words. In clear weather, the potential increases as we go higher, at
least for certain parts of Europe, and there is a diurnal and annual
variation of this quantity which the presence of fogs causes also to vary.
The first observers were inclined to attribute the electricity of the
atmosphere to the evaporation of water, and an old experiment which
consisted in dropping a ball of red-hot platinum into water placed on a
gold leaf electrometer, was supposed to confirm this view. Even re-
cently a distinguished physicist held this opinion in the case of electric
storms. Now when a ball of platinum is thus dropped into water, the
excessive commotion thus produced will certainly give rise to electricity;
but to assert that this electricity is due to evaporation may very well
be an error. It is true that occasionally a red-hot meteorite may fall
into the sea, reproducing thus the laboratory experiment; but most of
the water is evaporated quietly. Eecently one of my students used
under my direction a Thomson quadrant electrometer in order to inves-
tigate this question, and although he evaporated large quantities of
different liquids, he did not find any trace of electrization. I hope to
prove thus conclusively that the electricity of the atmosphere cannot
be the result of evaporation.

Sir William Thomson thinks that the experiments which have been
made hitherto indicate that the earth is charged negatively. This con-
clusion would certainly explain all the experiments hitherto performed
in Europe; but the only method of reaching certainty on this point is to
execute a series of experiments on the whole surface of the globp, and
it is this method that I propose to-day. This series of experiments
would furnish data for determining not only the fact of terrestrial
magnetism, but also by the aid of Gauss's theorem the amount of the
charge on the solid portion of the earth; however, this amount cannot
be determined for the upper atmosphere. What we want to know is
the law according to which the electric potential varies as we ascend
on the whole surface of the globe and at the same instant of time, so
that it may be possible to obtain the surface integral of the rate of
variation of the potential over the whole globe. If the oarth were ever
to receive an increase of charge coming either from the exterior or from
the upper atmosphere, this increase would be known. When, in the
London Physical Society, I criticized the theory of Profs. Ayrton and
Perry on terrestrial magnetism, I gave at the end of my paper a brief
outline of a recent theory on auroras and storms, which was built on
the hypothesis of the electrization of the earth. After mature reflec-

214

Henry A. Rowland

tion I still wish, to present to yon this theory, which deserves to be
thought of in mapping out a system of international exp.eriments on
atmospheric electricity.

Suppose Sir William Thomson's explanation is correct and that the
earth is charged with electricity, let us examine what would then
happen. If the earth were not exposed to disturbing causes, a portion
of the electricity of the globe would discharge itself into the atmosphere
and would distribute itself nearly as uniformly as the resistance of the
air would allow. The exterior atmosphere thus charged would set itself
in motion, and we should have winds produced by the electric repul-
sions, and this would last until the electricity had been distributed in a
uniform manner on the earth and in the exterior strata of the atmos-
phere; when all would be stiU once more. An observer stationed on the
earth would have no idea of the charge of the exterior atmosphere; but
he would discover the charge of the earth by means of the ordinary
instruments used in experiments on the electricity of the atmosphere,
such as Becquerel^s arrows and Thomson's water dropping apparatus.
There would be another result which however could not be measured by
observers situated on the earth, namely, the extension of the atmos-
phere beyond the limits determined by calculation. The rarefied air
being electrified would repel itself, and possibly there would be then in
the exterior atmosphere a region in which the pressure would vary s’^ery
slightly for a great difference of elevation. We have learned from
auroras and meteors that the atmosphere extends to a much greater
distance than that indicated by Newton^s logarithmic formula, but I
^'hi-nTr that what I have said is the first rational explanation of this fact.

Observe now what would happen if the earth of which we speak wore
subject to the disturbing causes which exist on our globe; the most
important of these disturbing factors are the winds and the general
atmospheric circulation. This circulation constantly carries the atmo-
sphere from the equator to the two poles, but with very little uni-
formity. However, near the poles there must be many points at which
the air comes down towards the earth and thus shapes its course towards
the equ’ator. Now a body which is a bad conductor, like air, when it is
charged tends to carry its charge along with it wherever it goes, and
thus the air carries its charge until the moment when it descends
towards the earth; then it will leave it behind in the exterior atmo-
sphere, in accordance with the tendency of electricity to remain at the
surface of charged bodies. The charge will therefore accumulate in the
exterior atmosphere, until there is a great tension; the atmosphere

On Atmosphbkio Eleotbioity

216

will then discharge itself either towards the earth or through the rare-
fied air in the shape of an aurora. At these points the rarefied air
probably heaps itself up to a greater height than elsewhere, which
would explain the great height at which auroras are sometimes observed.

The equilibrium which existed previously at the equator would also
be destroyed by the absence, at this point, of the primitive charge in
the exterior atmosphere, and the earth would have a tendency to dis-
charge itself towards the exterior atmosphere. Owing to the difference
in the conditions at this point, this tendency will be apt to show itself
by the storms which arise oftenest in the equatorial region. Thus the
electricity of the earth would tend to circulate in the same way as the
air from the equator to the poles and conversely.

But I do not intend to insist upon this theory here; I wish simply
through it to bring out the importance of establishing on the whole
surface of the globe a system of general observations on atmospheric
electricity. Even if the theory is false, it is only by observation that
the truth can be attained. In my opinion, it is almost unworthy of the
advanced state of our sciences to-day, that it should be at present impos-
sible for lis to indicate accurately the origin of the energy which mani-
fests itself in auroras and storms. For I have pointed out above that
it is necessary to give up explaining these phenomena by the hypothesis
of the production of electricity by evaporation.

I propose therefore that from this section of the Congress a com-
mittee be formed to examine what is to be done in order to establish
on the whole earth, and especially in the polar regions, a systematic
series of observations on atmospheric electricity.

Editoeial ITote. — International Commission of Electridans

[Professor Rowland sailed from New York, October 14, to attend an
international commission of electricians, then about to assemble in
Paris. Professor John Trowbridge of Cambridge sailed about the same
date. These two gentlemen were selected to represent the United
States government by the Department of State — Congress having made
provision for the appointment of two civilian commissioners.

This official commission is the outgrowth of the congress of electri-
cians which was held a year ago in Paris. That body requested the
French government to invite other nations to unite in constituting
three international commissions for the study of certain specified
problems, namely:

I. A re-determination of the value of the ohm.

216

Hbnby a. Eowland

n. (a) atmospheric electricity.

(6) protection against damage from telegraphic and telephonic
wires — (paratonnerres),

(d) the establishment of an international telemeteorographic

line.

III. Determination of a standard of light.

The study of atmospheric electricity was proposed to the congress by
Mr. Eowland. After hearing his paper on this subject, the section to
which he belonged adopted on his motion the following resolution which
was subsequently approved by the entire congress.

Resolved that an international commission be charged with determin-
ing the precise methods of observation for atmospheric electricity, in
order to generalize this study on the surface of the globe.

As Mr. Eowland did not retain his manuscript, the foregoing trans-
lation of the paper as it is printed in the Oompies Bendus of the con-
gress has been made by Mr. P. B. Marcou and is printed here with the
author^s consent.]

THE DETERMINATION OP THE OHM

Extkait d'unb Lettub de M. IIenkt a. Rowland

[Oonfirence Internationale pour la BeUrmination dee XJnith illectriquee. Proc^.B-y6r-
bauz, Deuzidme Session, p. b7, Paris, 1884]

Les exp6riences relatives k la determination de Tohm ont 6t6 pre-
paries k Baltimore an moyen d’nne partie du credit de 12,500 dollars
alloue dans ce but, rann6e derniere, par lo Congres des Etats-ITnis.

Apris nne 6tnde priliminaire, les appareils destinis k cos exper-
iences ont ete mis en construction en juin 1883. Les autorit6s de
rXJniversite Johns Hopkins ont bicn voulu mettre k ma disposition
nne construction qui est situie en dehors de la ville, k Tendroit appeli
Clifton, et qui a iti transf ormie en laboratoirc.

La source d’61ectricit6 qui servira aux experiences est une pile
secondaire du systime Plante, chargic par une machine dynamo-61ec-
trique actionnie par une machine k vapour d’environ 5 chevaux do force.

Trois methodes au moins seront employees pour la determination
de Pohm. La premiere repose sur Finduction mutuclle dc deux circuits;
j^ai deji fait usage de cottc mithode en 1878, mais dans les nouvelles
experiences les dimensions des appareils seront considerablomont aug-
mentees; les bobines auront un mdtre do diametre.

La deuxieme m6thode est bas6o sur rechauifement d’un conducteur
par le courant eiectrique, le mSme fil 6tant echauffd successivement par
le courant et par des moyens m6caniques. Les appareils employes
seront ceux qui m^ont servi, en 1870, pour determiner r6quivalont
mdeanique de la chaleur. Aiin d’evitcr les pertes, le calorimetre sera
rcmpli d’un liquido non conducteur au lieu d^5au. Pour mosurer
renergie eiectrique, on a construit un 61octrodynainom6tro ayant des
bobines d'un metre de (liam6tre.

La troisieme rndthode est cello de Lorenz. Pour determiner la
Vitesse du disque, il sera fait usage d’un diapason mil par un m6canisme
d^horlogerie, construit par Ivdnig, de Paris.

La comparison do Tunite de TAssociation Britannique avee Funitfi
mcrcurielle est pifis d’Stre tenninde; on dehors de cola, aucun rdsultat

S18

Hbnby a. Eowland

n^a 6t6 obtenu jusqu’S. present, mais je crois pourvoir dormer mes r6-
sultats d^finitifs en novembre.

Oomme ces experiences seront faites avec les precautions les plus
grandes et dans des conditions tr^s farorables, gr^ce k la gen6roBite du
Congres, il est k esperer qu^aucune decision concemant la valeur defi-
mtive de Tohm ne sera prise avant cette epoque; de cette maniere, les
Iltats-TJnis et d’autres pays pourront accepter retalon arr§te.

Hjenet a. Eoitland.

THE THBOEY OF THE DYISTAMO

IBeport of the Mectrical Conference at Philadelphia in UTovember^ 1884, pp. 72-88, 90, 91,

304-107, Washington, 1886 ; Electrical Beview (N. T.), November 1, 8, 16, 29, 1884]

I will now proceed with the discussion of ‘ The Theory of the
D 3 mamo-Electric Machine.’ I only claim in the skeleton of the theory
which I have here prepared to give a few points which may be of inter-
est and possibly of value to those who are constructing these machines.

The principal losses of the machine I put down under the following
heads: (1) Mechanical friction; (3) Foucault currents in the armature;
(3) energy of the current used in sustaining the magnet; (4) self-induc-
tion of the coils; (5) heating of the armature.

Of course the eflSiciency of the machine would be equal to the whole
work of the machine minus the different losses divided by the work,
namely:

E =

•uf

Thus, when the losses are known, the efficiency of the machine is
known.

The mechanical friction I shall not discuss.

With respect to Foucault currents in the armature, by dividing up
the armature in the proper way, we can get rid of most of these. It is
very often effected in the Siemens armature by dividing up the arma-
ture into discs.

I have purposely omitted the loss due to change of magnetism in the
armature as the armature revolves. 1 drew attention to this fact sev-
eral years ago. It has been recently experimented upon and found
that, although there is some heating effect, it is very small indeed.

With respect to the energy itscd in sustaining the magnet, if the
magnet were of steel there would, of course, be no loss. The only
reason for not using a steel magnet is that the field is comparatively
weak. The field of a steel magnet is, I suppose, leas than one-third of
the field due to a good electro-magnet; the two could not be made
equal by any possible moans. Therefore, in most dynamo machines,
the magnet is produced by the current.

S30

Henry A. Eowland

It is a question what the form of the magnet ,and the position of
these coils should be in order to get the greatest field with the least
expenditure of energy. I have one or two propositions to make on this
subject which I think are of some interest.

The first proposition I have to make is that a round magnet is better
than one of elongated cross-section. If the coils are long, and they
are usually long enough for the purpose, although the theory assumes
an infinite length, the magnetic force at any time acting on a round
iron core is exactly the same as on an elongated core. But the area
of a circular section is much greater than that of an elongated section
of the same circumference, and therefore the same amount of wire
which would be used to go around the elongated magnet, would, if
extended on a circular section of the same circumference, surround
much more iron.

The principal object of making an elongated magnet is that it may
include the whole length of the armature. Most makers who ■ adopt
this form think it better to elongate the cross-section than to have a
long pole piece. But we have seen that the round form is more efidcient
in general than the elongated form, and the only question is whether it
will be more efficient in this particular case. I shall proceed; in this
theory upon the known fact that we can consider lines of force as if
they were conducted by the iron and the air outside. The conductivity
of the iron for the lines of force is very great, much greater than that
of air. I experimented on it many years ago, and my idea is that it
varies (according to the degree of magnetization) from several hundred
up to fi,000 times that of air. The conductivity for iron is very great,
especially for wrought iron; for cast iron it is probably less. Therefore
the lines of force will be conducted down through the iron from any
point over a circular cross-section very nearly as easily as they are from
an elongated cross-section, and the saving in the wire will be con-
siderable.

I have another proposition to make with respect to the magnet, and
that is that one circuit of the lines of force is better than a number.
There is a loss from having a number of electro-magnets, even if they
are round. For this reason, that the same magnetic force is acting in
each of these coils provided there is the same number of wires per unit
of length; and the same wire will go more times around the same iron
concentrated in one magnet than when subdivided into several, and
will, therefore, act upon it with more magnetizing force.

That proposition not only applies to this form of . magnet (Fig. 1),

The Theory or the Dynamo

Z21

■but it also applies to the form where we have the armature revolving
between two magnets like this (Fig. 2), because we can turn this lower
magnet over and bring the two together. The circuits of the lines of
force are around in this direction and in this (arrows, Fig. 2). So that
there are two circuits of the lines of force instead of one. The energy
expended for a given amount of work will be less with this form (Fig. 1)
than with this (Fig. 2). That is of very great value to makers of
machines.

The theorem applies to a number of those old machines where there

Eio. 1. Fig. 2.

was a very largo number of little magnets revolving around other little
magnets. More work is used in sustaining the magnets in that form
of machine than in the more modem form where we have only a few
circuits.

I had a number of drawings made of magnets in the Electrical Exhi-
bition, and I find very great difference in this respect; more difference
where Siemens armatures are xised than in any other kind. In dis-
cussing these drawings I do not give any names, nor say whether one
machine as a whole is better or worse than another.

First, I will discuss the general forms of the magnet, and then I wish
to say something in resfpect to the form of the pole pieces that inclose

222

Hbnet a. Kowland

the .armature. Of course this form belongs both to the Gramme ring
and the Siemens armature. Most modem machines are of this nature,
either Gramme or Siemens, and we may consider them both one if
we wish.

We vill now proceed with respect to the field in this form of magnet
(Fig. 3). The lines of force proceed down the magnet, and are sup-
posed to go across here (a J), where wires wound around the revolving
armature cut them, and so produce a current. It is evident that any
Imes which escape across this open space (arrows) are lost. If there

Fig. a. Fig. 4.

was any leakage of the wire around the magnet, the current, instead of
going around the magnet, would go off somewhere else, and we should
consider the machine defective because there was a loss of the current.
So if any of these lines of force, instead of going directly across there
(a J), go across the open space (arrows), as they naturally would do, all
those lines of force are lost, and we would have to add so much more
current in order to make up for this outside loss. I have an illustra-
tion of such losses of lines of force from a drawing, which I *^11 give
you (Fig. 4).

This machine has two magnets — one above and one below. The lines

The Theory op the Dynamo

223

of force pass up through here (alcd) and then out and around through
here (ee), &c., to complete the circuit. As I saw the machine in the
exhibition these outside pieces (ee) were closer to the poles of the
magnets than I have drawn them. If they are put too near, some lines
of force, instead of passing across the field of force, whore the wires
revolve, as they ought to do, pass off at these openings, the circuits
going around in this way (arrows f f). In this case there is a loss due
to leakage of the lines of force, and we shall therefore have to expend

Fig. 6. Fig. 0.

more energy in keeping up the magnet. There is energy expended in
keeping up the field outside as well as in keeping up the field through
the armature. It is important that this point should be consideted.
These questions, ^ How many lines of force go across this opening and
are effective in producing the current, and how many escape off without
passing through the opening and are lost?^ are just as important as
the question of the leakage of the current in the wire. There are
defects in many of those machines in that respect. In this form of
machine (Fig. 1), where there is a simple circuit, this magnet has to be

224

Henrt a. Eowland

attaclied somewhere. Very often the magnet is turned vertically, poles
downward, and attaclied to a cast-iron bench. I have no doubt that
some lines of force are lost (not much perhaps) in passing across from
the magnet to this iron bench. The makers of the machine, I suppose,
considered this to some extent, but what is needed is measurement on
that point.

Here is another form of magnet (Pig. 6). That machine would be
defective. It has two magnets and two magnetic circuits in the place
of one, and many of the lines of force probably make little private cir-
cuits of their own around in that way (arrows). Those lines of force
are of course lost, and it is more or less defective in that respect. It
would be better to diminish the number of magnetic circuits to one.

(I am only giving a general idea of the principle of these machines,
and I do not refer to any in particular.)

It is also important that these lines of magnetic induction shall find
easy passage around in order to produce the most intense field. Thus
the opening between the armature and pole pieces must be made as
small as possible, in order that the lines of force may find easy passage
across it. Everybody recognizes that. Suppose we had a machine made
in the following manner (Pig. 6), in which there is a magnet with
a Gramme ring here (a), and pole piece here (6), a ring here (c), and
pole piece here (<i), but no pole pieces opposite these. How are the
lines of force to pass around ? I do not know that it would be easy to
see how. They evidently go around "here (arrows) and get to the other
side the best way they can. There is no easy passage around for the
lines of force in this case.

A Member. May they not to some extent follow the shaft?

Professor Eowland. It is evident that if the shaft is made large
enough some go along the shaft in that way (arrows), but there is no
easy way for them to get around.

I have here a formula for the amount of work which one has to
expend upon a magnet in order to produce a certain effect. I will take
the case which I have considered most eflBcient, where there is one
magnetic circuit. It is an original idea of Faraday that these linos of
force are conducted. We suppose the lines of force to pass through
the iron and across the opening in this way (arrows, Fig. 1), and they
are caused to do that by what may be called the magneto-motive force
of the helix-

I will just obtain an expression -for the number of lines of force B,
This is not the quantity which Maxwell considers, but it includes the

The Thbobt op the Dthamo

225

whole niunber of lines of force which pass through the magnet. We
may write B, proportional to iV, the number of turns of the wire around
the magnet, and 0, the current; and inversely proportional to the re-
sistance to these lines of force in gomg around the circuit. The resist-
ance to the lines of force is proportional to £, the length of the iron of
the system, divided by S, the cross-section of the magnet, supposing it
to be uniform, into /u, the magnetic permeability of the iron (or the
conductivity of the iron for the lines of force). This quantity ju varies
with the current, and can readily be obtained. Some years ago I gave
a formula for it. It can be expressed simply as dependent upon the
magnetization of the iron and a constant depending upon the iron
alone. We have something more to add:

Let Z be twice the width of the opening between armature and pole
piece, and A the area across which the lines of force flow: then we

have to add and another quantity, which we can call p, which depends

upon the resistance of these lines of force which escape in all direc-
tions and represents the loss due to that escapement. Thus we have
the final value for the number of lines of force (or rather induction)
in the magnet

/Sa ^ -4 -}- p

This gives us an equation which may be solved with respect to /jl.
The curve for the magnetic permeability is of this nature (Mg. 7). It
will be of a more or less flat form, according to the value of Z and p.
Therefore, in increasing the magnetic force upon the magnet, it becomes
easier and easier to magnetize it until a certain point is reached, and
after that it becomes harder and harder. In practice the core should
have sufficient cross-section to produce a very strong magnetic field,
but not so great as to requne too much wire to wind it. The two must
be balanced, which can only be done by calcixlation or, better, by experi-
ments on the machine. By examining the force of the magnet at each
point, and in that way getting an idea of how these lines of force go,
we can see whether the cross-section of the core is large enough to
produce all the lines of force necessary for our purpose or not. Of
course, in order to have suflScient magneto-motive force to send lines of
force across the opening in sufficient quantity, we must have sufficient
wire. As the thickness of the coil is increased, we have to use more
wire in proportion for a certain diameter of core, which is a disadvan-
16

226

Hbnbt a. Eowland

tage, since each coil acts Very nearly the same as every other in produc-
ing force. But if the core is very short indeed, wire must be piled on
it to a very great extent in order to get sufiScient magneto-motive force,
and as iron is cheaper than copper it might be better to lengthen out
the core. I do not know where the lengthening should end, but I
should suppose when the requisite wire on the magnet makes a moder-
ately thin layer. Of course, as we lengthen out the magnet, the resist-
ance of the circuit to magnetization becomes greater; but that is a very
small quantity. I do not suppose the increase is very much for a
considerable lengthening of the magnet. As I said before, ’the magnetic
conductivity of iron is many times greater than that of air, and we can
lengthen out the cores without producing much loss on account of that
lengthening.

Some persons have suggested that there might be a slight gain from

the fact that iron, after it has been magnetized a great number of times
in the same direction, rather likes to be magnetized in the same direc-
tion afterwards. If the core is made of any material similar to steel,
such as wrought iron or anything of that sort, it might be possible to
have some gain from the coercive power of the magnet. There would
be loss from that cause at first; but from the continual use of the
machine I think it very likely the iron might get a set in the direction
of the force. If the core were of steel, for instance, it might be that
one could send a strong current through at first and magnetize the steel,
and then be able to diminish the current considerably and still keep up
a very large magneto-motive force. I do not know how practical that
would be, but it seems to me that one could produce a very strong field
in that way. In the commencement of the operation of the machine,
we would have to send a powerful current to magnetize the steel, and
then, without stopping the current, to diminish it. Then the set of

The Theoe*y of the Dynamo

227

the steel ■would be in the same direction with the current and produce
the field with less expenditure of energy than if it were simply iron.

There is no difference between a shunt and a series machine. The
magnetizing force on the magnet I have set do'wn as proportional to the
number of turns multiplied by the current; that is, proportional to the
cross-section of the coils multiplied by the current per unit of cross-
section, so that the magnetizing action can be the same either from a
strong current or a weak current. Therefore, if the exterior dimen-
sions of the coils are the same in both cases, the same energy is ex-
pended in each in order to produce the same force, so that there is no

Fig. 8.

difference between a shunt machine and a series machine as far as the
economy of the magnet is concerned.

I do not wish to take up too much of your time, and will go on to
the heating of the armature. Of course the amount of energy expended
in the heating of the armature will be dependent on the resistance of
the armature. It is well known that the efl&ciency of the circuit will
merely depend upon the relation between the resistance of the arma-
ture and the exterior circuit.

There is one other point in regard to losses; ' dead wire,'* I think, is
the technical term for it ; I mean that portion of the wire which does
not cut the lines of force. In the Gramme pattern the armature is

228

Hbnbt a. Eowland

inside of the rings. In the Siemens pattern the coils are around the
ends of the armature. In a section of the Gramme ring (Fig. 8), the
outside portion of the wire (a) is active, since the lines of force follow
the core and the outside of the ring around; but the lines of force do
not go through the core of the ring, so that the inside portion (6) is
dead, so that we can say nearly ‘half the wire is dead wire. In the
Siemens armature one cannot see immediately how much dead wire
there will he, because it depends upon the length of the armature. The
wire is wound around in that way (Pig. 9), and this portion {a a) is
active, and this portion (6 h) is dead. If the armature is very thick we
would have more dead wire than when it is simply long. I cannot say
which has the more dead wire, but I dare say the Gramme has more

Fig. 9.

than the Siemens. Furthermore, either in the Gramme ring or the
Siemens armature (Fig. 10) we have the lines of force running across
here (arrows) ; that portion is active; but these portions (a a) in between
the poles are dead, and when the armature revolves we have the lines
of force turning around, and I think that would add more dead wire.
I believe an attempt has been made to throw out these coils.

There is no necessity to go further. As I have said, the efficiency of
the circuit depends upon the ratio of the resistance of the armature to
the resistance of the wires, and therefore, as far as this point is con-
cerned, any machine can be made as efficient as one pleases by putting
in greater apd greater external resistance. But as the magnet remains
the same, we would jdnd a point where the efficiency as a whole would
not increase for an increase of external resistance, but would actually
diminish. There are other things to be taken account of, such as losses

Thb Theobt of the Dts-amo 229

<3.116 to the self iaduction of the coils Thich produce sparks in them.
I have requested Professor Fitzgerald to take up that point, and will
leave it for him to consider.

There is another point with regard to the dynamo which can he
•treated in this simple manner with no use of the calculus. This is
-very simple reasoning if you only know the principles. I shall con-
sider two machines similar in all respects, except that one is larger than
-tile other, or rather consider one machine, and see what the effect will
Tse when that machine gradually changes in size.

The point from which we start shall be that the magnetic field is con-
stant in the two machines. For, owing to the fact that there is a limit
in the magnetization of a magnet, we cannot have a field with more

Fio. 10.

±h.an certain strength produced by iron, and I will suppose that the
strength is reasonably near that maximum for iron. It cannot be up
•to the maximum strength, of course, but somewhere near it. I made
some experiments many years ago upon an ordinary magnet, the results
of which were published in Silliman’s Journal, by means of what I call
the magnetic proof plane. (Am. J. Sci., vol. 10, 1876, p. 14.) It
applies beautifully to dynamo machines, and I obtained everything with
it that I have referred to here. If I remember right, I found in that
zxiagnet about one-third of the field that an iron magnet could pos-
siWy have.

It is theoretically possible to get a force equal to the magnetizability
of the iron, but practically, I suppose that instance is about the case
of the ordinary d 3 mamo machine. We start, then, with the supposition
•that the field of force in the two machines, one of which is larger than

230

Hbnet a. Eowland

the other, is constant. That is to say, the magnetizing force at any
point of one machine is eqnal to that at a similar point in the other
machine. In making a drawing of the machines, it would not matter
about the scale of dimensions; the force at a certain point is a certain
amount whatever the scale.

Next consider what must be the current through the wire in the two
machines. There are the same numbers of turns of wire around the
magnet, and everything is the same except the dimensions. Consider
the current passing around the coil of a tangent galvanometer. If the
galvanometer grow, in order to produce the same effect at the centre
(and not only at the centre but at every point), the current must in-
crease in direct proportion to the radius of the coil. When the coil is
twice as large the current must be twice as large, in order to produce
the same force at every point. Thus, if -there is no difference in the
material of the two machines, we have their currents in direct propor-
tion to their linear dimensions. Make a machine twice as large and
the current in the coils must be twice as great to produce the same
magneto-motive force. Of course the wire has increased in size; if
the machine has increased to twice its original size the cross-section
of the wire has increased four times. In other words, from that cause
the current per unit of area will vary inversely as the square of \ the
linear dimensions; and since we have found the current to vary directly
as Z, in order to retain the same force in the field, by a combination of
the two results, it varies inversely, as Z. Therefore, so far as the
magnets are concerned, the heating effect, which depends upon the
current per unit of cross-section, will decrease with the size, while the
surface will increase in proportion to the square of the size. There
will, therefore, be less danger of heating in a large magnet than in a
small magnet, but this is only with respect to the magnet.

The resistance of any part of the machine varies, of course, directly
as the length of the wire, and inversely as the cross-section. The cross-
section varies as Z®, so that resistance varies inversely as Z. Therefore
the larger the machine the less the resistance; one machine being twice
as large as the other, the resistance will be half as great. This applies
not only to the work of the magnets, but to the work of the armature.

I will now consider the electro-motive force. The electro-motive
force is proportional to the product of the current and the resistance,
or we may write B = RO, We have the current proportional to Z, and
the resistance inversely proportional to 1; therefore the electro-motive
force is constant. As we are running the machijie, it turns out that

The Theory oe the Dystamo

331

the electro-motive force does not vary -vrith the size, but -we shall pres-
ently see how this is modified so as to get greater electro-motive force
for the larger machine.

The work done is C^B in any part of the machine, or in the wliole
machine, just as you please. This varies directly as 1. Therefore the
one machine which is twice as large as the other requires twice as much
power to run it, and twice as much electrical energy comes out of it.
But it is to be remembered that the weight of the machine varies as P,
and we only get work proportional to I out of it.

So far as results go, we have constructed two machines which differ
only in size. The efficiency of these two machines is a constant quan-
tity. That will be rather startling to some, who think a large machine
is more efficient than a small one. As far as we have gone in any two
machines, one of which is simply larger than the other, the efficiency is
the same.

But if we calculate the angular velocity of the armature to keep the
proper current we shall find that it varies inversely as the square of the
linear dimensions. In other words, in one machine twice as large
as another the velocity of the armature must be only one-fourth as
great in order to produce the proper current in the wires. This takes
account, I think, of every irregularity in the machine. The two
machines are exactly the same in every respect. I have not added the
loss for the self-induction of the coil. I have an idea that this also
should be taken into account, but Mr. KLtzgerald will consider that
I)omt.

How the question comes up, can we increase the velocity of the arma-
ture above that point ? Is it practically necessary that we should run
cue machine at one-fourth of the angular velocity if it is twice as large?
It is a practical question; but I should certainly think the velocity was
not in that proportion. I should think it would be more nearly in-
versely as the size and not inversdy as the square of the size. If so,
then by so arranging the wire of the armature as to iucrease the pro-
portion of external resistance we can have the same current per unit
of section when running the armature faster and the same electro-
motive force. If we do that, this whole theory applies; but we shall
have increased the external resistance of the machine in comparison
with the resistance of the armature, and when we do that we increase
the efficiency of the machine.

I think it is from this cause that we find large machines more efficient
than smaller ones; but it is also evident that there is a limit to this.

2S2

Hbnet a. BowiiAOT

vHch can only be obtained, I suppose, from practically making the
machines and seeing how much faster they may be run without flying
to pieces. As far as this theory goes, the increase comes not from the
size of the machme, but from the fact that we can get a greater electro-
motive force with the same angular velocity, and so can reduce the
internal resistance in proportion. In very large machines we can make
the wire with one turn, not several turns — simply bars on the machines.
We thus decrease the resistance of the machine, and at the same time,
if we run it above this proportion which I have pointed out, we obtain
the proper electro-motive force. In other words, the proper electro-
motive force is more easily obtained from the large than the small
machine, because it is not practically necessary to decrease the velocity
so as to keep it inversely as the sqixare of the size.

[Discussion by Professor Elihu Thomson and others.]

With respect to Mr. Thomson's remarks, I am very glad to see the
matter taken up in this spirit and to have my principles intelligently
criticised. However, there was one remark which I wish to state imme-
diately as an error, of course, with regard to the steel. Steel can be
magnetized to exactly the same degree as soft iron. There is no differ-
ence between soft iron and steel in that respect, except that we require
an immensely greater force to magnetize steel to the same extent as
iron. There are some old papers of mine, which were published in the
" Philosophical Magazine,^ I believe, in 1873, relating to experiments
where I took iron and steel and several other metals, and showed that
the maximum magnetization was the same in all cases.

But with respect to a number of statements with regard to flat mag-
nets and round magnets I am very glad to see my remarks criticised in
the manner that they were, because it shows the need of exactly what
I stated; and that is experiments upon this subject. The question is
one of quantity. My reasoning gave results in one direction, and Mr.
Thomson gave reasons for making the magnet in another way, and it is
a quantitative question of course as to which is the best; and for that
reason I want very much to see experiments made in the manner whicjh
I have described by means of this "magnetic proof plane," so as to find
out what the escape of the lines of magnetic force in all cases is.

I think we can decide on one point that was brought up without any
trouble, and that is with respect to the dynamo made with extended
pole piece (Fig. 2), where it was assumed that the lines of force liad a

The Thboet of the Dthamo

233

tendency to go in a particular direction, that it was a sort of gun shoot-
ing the lines of force through the armature. That is not true, because
they do not have any tendency to go that way at all, and we would only
add that much to the area of the end of the magnet. Very few lines of
force will go out there, and by putting this additional magnet on we
add to the area of the magnet. The lines of force will go out at the
sides probably in greater numbers than they would at the end, so that
I do not thi^ that particular objection holds in that particular case.
It is a question of quantity ; the thing should be measured and found
out- I see very plainly in my own mind that more lines of force would
go out the side by adding this iron here (Pig. 2 ) than would go out at
the end of it by leaving it vacant, as in Pig. 1. But it is a matter of
mere opinion. Another reason for having fewer magnets is that the
surface is greater in the case of the larger number than of the smaller
number for the lines of force to escape from.

There was another point brought up here with respect to the machine
which was made in this way (Pig. 4). It was stated that there was
some gain from the magnetic action of this coil on the iron outside.
There is undoubtedly a gain : the question is how much, and whether
more lines do not escape than would make up for that. With no
experiments to go on, it is a case of judgment. My own judgment
would be that there would be very little gain; but, as I said before, the
thing should be measured, and then we could find out about that point.

[Discussion by Professors Sylvanus Thompson and Anthony and
others.]

I am very glad that that point of hollow magnets has been brought
up, as I think that the question of hollow magnets, hollow lightning
rods, and a great many similar things, causes more difficulty, especially
to practical men, than almost anything else. It can be explained in
a very few words. Take a hollow bar having the magnetizing coil
around it acting to send lines of force along it. They have got to go
out to make their complete circuit. They could only end at a certain
point if we had free magnetism, that is, a separate magnetic fluid.
I speak not from a physical sense but from a mathematical point of
view. The principal resistance to the propagation of these lines of
force is in the air and not in the magnet. If we take away a large
portion of the interior of that magnet we will have the surface the
same as it was before, and consequently the external resistances are the

?34

Henet a. Eowland

same. In such a case as that we leave the magnet about as strong as
it was before. But that would not be the case if we compress magnet-
ism until we get it up to the point of magnetization of the centre. In
that case we should need the whole mass, and it is almost impossible
to magnetize to any extent without the centre coming in. It depends
on the length of the bar. If we bring the bar around, making a com-
plete magnetic circuit of the thing, so that the lines of force do not
have to pass out into the air at aU when we put a wire around it so as
to wind it like a ring at every point, in that case the whole cross-section
becomes equally magnetized, i£ it is not bent too much. If it is a large
ring of small cross-section, it is perfectly magnetized across from side
to side. We know that perfectly well; it is a result of the law of con-
servation of energy. The case of dynamos is like that. We require
the whole cross-section to transmit these lines around. The resistance
to the magnetization comes partly from this opening and partly from
the iron. We have no gain in making these cylinders hollow; indeed
we rather increase the outside surface to let lines of force flow into the
air. In the case of a dynamo machine, the solid form is not only
desirable, but by far the most ejficient.

I have thought of that matter a great deal, and experimented upon
it. Indeed this closed circuit is the very idea from which the permea-
bility of the iron is determined. All the calculations upon that sub-
ject are based upon that law. I think there can be no doubt that in
the dynamo the solid form is the proper form, and that the whole cross-
section is effective. The whole cross-section of a round piece is just as
effective as the whole cross-section of a flat piece. The flat piece ex-
poses more surface to the air, and there is more surface for the force
to escape from. That is another reason for not making the magnets
flat. The round form is that in which there is the least surface, and
therefore the least liability of the lines of force to escape. You can
conduct the lines of force by a round piece to any point you desire much
better than by a flat piece.

[Discussion by Professor Sylvanus Thompson.]

I do not know that the theory bears upon the solidity of the core.
Of course, the more iron in there the better is the efficiency of the
machine. I suppose there would be no objection to dividing that
cylinder up into a number, so that the Foucault currents could not
exist, if the exterior form was round; but I do have an objection to

The Thboet of the Dynamo

2Zb

making it any other shape. Indeed, currents could be more thoroughly
eliminated by dividing up the cross-section than by making it of a
very elongated form.

[Discussion by Professor Blihu Thomson.]

I do not like to rise so often, but I think there is some misapprehen-
sion. I have not said anything about large masses of iron. There are
the same masses of iron in my method as in any other. The only
question is as to making them round or elongated. Of course by
dividing this core up it becomes similar to a core of the Euhmkorft
coil, and the currents change very rapidly. From Professor Sylvanus
Thompson’s remarks, I thought that that was desirable. One cannot
say that the current is transferred from the core to the wires outside.
The same current might take place, and, if the resistances are the
same, would take place in the wires outside in both cases. By lengthen-
ing the time of action one decreases the electro-motive force or de-
creases the external current. If the time is ten minutes one would
have one electro-motive force for the external current; if it is five
minutes, the electro-motive force would be somewhere near twice as
great as before, the whole quantity of electricity passing being the same
in both cases.

ON LIGHTNING PEOTBCTION

[Biport of 13)0 Meetrieai Confertnet at Philadelphia In Noyenher, 1884, pp. 173-174 ;

Washington, 1886]

As this is an important question, especially in some of the Western
States, I mil say a few words.

In order to protect bmldings from lightning we must have a space
into which the lightning cannot come, and have the house situated in
that space. What sort of a space do we know in electrical science into
which electricity cannot enter from the outside ? It is a closed space —
I mean a space inclosed by a very good condheting body. All the light-
ning in the world might play around a hollow copper globe and it would
not affect in the slightest degree anything inside the globe; but the
the walls of the vessel need not be solid metal. Of course, if solid, it
is all the better ; but if it is made of a net-work of very good conducting
material it would protect the inside from lightning strokes. A spark
striking on one side of such wire cage would find it easier to go around
through the wire of the cage to the other side than it would to go
through the centre. This is MaxwelFs idea, with reference to protec-
tion of houses from lightning, viz., to enclose the house in a rough cage
of conducting material. Suppose, for instance, this box is the house,
and suppose we start from the roof and run a rod diagonally to each
corner and thence down to the earth. We thus make a rough cage.
Of course there are openings on the sides; and if we wished to make a
better protection we could put rods down the sides wherever we wished.
IsTow, there is ground underneath the house, and the lightning might,
by jumping across the centre, find a good conductor through the middle
of the house and go down to the earth in that way. How do we prevent
that? By running the lightning-rods clear across underneath the
house. Then the lightning would find it easier to go around the house
than to jump across, even if there were a good conductor through the
middle. A house inclosed in a cage of that sort would be perfectly
protected, even if it were a powder magazine, or anything of that sort.
Of course, in the case of petroleum storage reservoirs, where fumes are
given off, there would be danger then, as the stroke might ignite the

On Lightning Pboteotion

337

fumes of the • petroletun. That would not be the case of a powder
luagaaine. The protection in that case could be made perfect.

It is not necessary to have lightniug-rods insulated. Indeed the
question is, can we insulate a lightning-rod? We may insulate it for a
sxnall potential, but lightning coming from a mile or two to strike a
house is not going to pay any attention to such an insulator; we may
just as well nail the lightning-rod directly to the house as far as that
goes.

1*lie idea of having the lightning-rods inclose the bottom as well as
-the sides of the house is very important, because we do not know, and
wo have no right to assume, that the earth is a good conductor. We
are perfectly certain if the earth forms a good conductor that then the
lightning cpuld go down at the sides into the earth. By inclosing the
house in a case both below and above we obviate all that difBculty, and
it makes no difference whether the earth is a good conductor or not.

I am glad of this public opportunity to say something with regard to
a peculiar form of lightning-rod; it is in reference to a form of a rod
shaped like the letter U. I think the idea is that the lightning strikes
on one side, and that it goes down and has inertia and flies up again.
The company which advocated this idea had the impudence to bring a
lawsuit against a scientific man who said it was a humbug. A company
of course can make a great deal of trouble to one man; but when there
is such a gross humbug as that around, one would like to imdergo the
danger of a lawsuit. There is nothing scientific about it; it will endan-
ger life in any house in which it is placed.

IVCr. SooiT. 1 would like to ask whether a building constructed of
iron would not be completely protected from lightning ?

Professor Eotviand. Yes, if it has a fioor of iron too. If a gas-pipe
came up into the centre the lightning might find it easier to go across
t-o the pipe than to go around. But if we made a fioor of iron the
lightning would find it easier to go around than across to the pipe. It
mtist be an entirely inclosed house.

Mr. Soon. Then would not a petroleum tank entirely constructed
of iron with an iron bottom be the safest inelosure possible for petro-
leum ?

Professor Rowland. The peculiarity of that is that the fumes of
petroleum are all the time coming out from the cracks. The whole out-
*»ide is probably covered with petroleum. I suppose also the ground is
saturated with petroleum. The petroleum ns fnr as the inside goes
would be perfectly safe.

238

Hbney a. Eowland

Lieutenant Fiszb. I would like to ask how far lightning obeys the
ordinary law of currents, whether it takes the path of least resistance
or not. Do high potentials always do that? In general across a nar-
row space the resistance is greater than going around by the iron, and
the question is, to what extent does the lightning obey the law of
circuits ?

Professor Eowlan’D. I would like to say one word more with respect
to petroleum. In the case of the tank you have a mixture of the petro-
leum vapor and air which probably would explode. Unless the tank was
a very good conductor there might be also a little spark in the interior,
not enough to hurt a man in there; but the smallest spark inside the
tank would cause an explosion. I am not certain whether the iron of
the tank is a good enough conductor to prevent every trace of spark in
the interior. Indeed, suppose we had a tank with a cover upon it.
That is supposed to be a closed vessel, yet the lightning would have to
pass from top to bottom between the cover and the tank, and perhaps
a little spark would take place in the interior; and possibly in going
from one of the plates of the iron tank to the other it may find some
resistance and jump over some small plate in the interior of the tank.
It would be a most difficult thing to protect.

With regard to that other question, lightning in the air, of course,
does not obey Ohm^s law; it is entirely a discontinuous anomaly. It is
like the breaking of a metal. A piece of metal is supposed to break at
a certain strain; but it does not always break then; it pulls out in
strings or something of that sort. One cannot measure the distance
and say the lightning is going to jump across that distance.

THE VALUE OF THE OHM

[Zo Tjumi^re Sleeij-iQiie, XX VI, pp. 188, 189, 477, 1887]

La Valeur de l’TTiiit6 de HSsistance de I’AsBociation Britannique.

A la demidre reunion de 1’ Association biitannique, le professeiiT
H. A. Bowland a donn4 la valeur definitive de I’unite de resistance
eiectrique de 1’ Association, telle qu’dle a 6t6 deterinin4e par la com-
mission am4ricaine. La valeur donn^e en 1876 6tait : unite B. A. =
0-9878 ohm.

Dans la derniere determination, on s’est servi dee methodes de Kirch-
hoff et de celle de Lorenz.

La premiere a donne ime valeur de 0-98(;4(i ± 40 et la seeonde 0-9864
± 18; son erreur probable est done de moins de la moitid de celle do la
premiere methode.

Le professeur Bowland a egalement determine la resistance d’une
colonne de meroure de 1 mm.* de section et de 100 centimetres de lon-
gueur, et a trouve 0-96349 unites B.A.

Valeur de lEtalon B. A. de I’Ohm, d'apx-es les Mesures de la Com-
mission, Amerioaine, par Bowland.

Les obseivations ont ete termindcs en 1884 ddje, mats les calculs
viennent d’Stre terminds et seront publids prochainemont. Bn 1786:

Bowland a trouvd 1 unite B. A. = 0-9878 ohm.

Kimball a trouve 1 unite B. A. = 0-9870 ohm.

Maintenant Bowland trouve par la mdthode de Kirchhoff et k I’aido
de 73 observations

1 unite B.A. = (0-98627 ± 40) ohms
et Kimball par la mdthode do Lorenz et an moyen de 43 observations
1 unite B.A. = (0-98642 ± 18) ohms.

Bn eombinant los deux rdsultats, on trouve que I’unite mercurielle est
dgale h 0-96349 unitds B. A., e’est-k-dire que Tohm de mercure cor-
respond e, une colonne de mercure de 106-32 cm.

Bappelons id los valeurs obtenues par diffdrentB physiciens et quf se
rapproohent le pins du reRultat ci-dessus:

240

Hbnet a. Eowland

Lord Bayleigh
Glazebrook . . .
Wiedemann

Mascart

Weber

106*25 cm.
106*29 cm.
106*19 cm.
106*37 cm.
106*16 cm.

ON A SIMPLE AND CONVENIENT POEM OP WATEE BATTEEY

Cimeriean Jmmial of Beimm [8], XXXIU, 147, 1887; mionophieal Magtuiue [5J,
XXIJTf JJ08, 1887 ; Jo/ms Hbpkiiis XTnlmnity (HrcnlarSy No, 57, p. 80, 1887]

For some time I have had in use in my laboratory a most simple,
convenient and cheap form of water battery whose design has been iu
one of my note-books for at least fifteen years. It has proved so useful
that I give below a description for the use of other physicists.

Strips of zinc and copper, each two inches wide, are soldered to-
gether along their edges so as to make a combined strip of a little less
than four inches wide, allowing for the overlapping. It is then cut
by shears into pieces about one-fourth of an inch wide, each composed
of half zinc and half copper.

A plate of glass, very thick and a foot or less square, is heated and
coated with shellac about an eighth of an inch thick. The strips of
copper and zinc are bent into the shape of the letter U, with the
branches about one-fourth of an inch apart, and are heated and stuck
to the shellac in rows, the soldered portion being fixed in the shellac,
and the two branches standing up in the air, so that the zinc of one
piece comes within one-sixteenth of an inch of the copper of the next
one. A row of ten inches long wiU thus contain about thirty elements.
The rows can be about one-eighth of an inch apart and therefore in a
space ten inches square nearly 800 elements can be placed. The plate
is then warmed carefully so as not to crack and a mixture of beeswax
and resin, which melts more easily than shellac, is then poured on the
plate to a depth of half an inch to hold the elements in place. A frame
of wood is made around the back of the plate with a ring screwed to
the centre so that the whole can be hung up with the zinc and copper
elements below.

When required for use, lower so as to dip the tips of the elements
into a pan of water and hang up again. The space between the ele-
ments being -jV uujhj will hold a drop of water which will not evaporate
for possibly an hour. Thus the battery is in operation in a minute and
is perfectly insulated by the glass and cement.

This is the form I have used, but the strips might better be soldered
face to face along one edge, cut up and then opened.

ON AN EXPLANATION OP THE ACTION OP A MAGNET ON
CHEMIOAL ACTION*

Bt Hbkbt a. Rowland and Louis Bbll

[Americcp Journal of Sdmce [8], XXXVI^ 89-47, 1888; Tliiloaophical Ifagaxim [5].

XXFJ, 105-114, 1888]

Id the year 1881 Prof. EemseD discovered that magnetism had a
very remarkable action on the deposition of copper from one of its solu-
tions on an iron plate, and he published an account in the American
Chemical Journal for the* year 1881. There were two distinct phe-
nomena then described, the deposit of the copper in lines approximat-
ing to the equipotential lines of the magnet, and the protection of the
iron from chemical action in lines around the edge of the poles. It
seemed probable that the first effect was due to currents in the liquid
produced by the action of the magnet on the electric currents set up
in the liquid by the deposited copper in contact with the iron plate.
The theory of the second kind of action was given by one of ub, the
action being ascribed to the actual attraction of the magnet for the
iron and not to the magnetic state of the latter. It is well known
since the time of Faraday that a particle of magnetic material in a
magnetic field tends to pass from the weaker to the stronger portions
of the j&eld, and this is expressed mathematically by stating that the
force acting on the particle in any direction is proportional to the rate
of variation of the square of the magnetic force in that direction.
This rate of variation is greatest near the edges and points of a mag-
netic pole, and more work will be required to tear away a particle of
iron or steel from such an edge or point than from a hollow. This
follows whether the tearing away is done mechanically or chemically.
Hence the points and edges of a magnetic pole, either of a pennanont
or induced magnet, are protected from chemical action.

One of Prof. Eemsen^s experiments illustrates this most beautifully.
He places pieces of iron wire in a strong magnetic field, with tluur
axes along the lines of force. On attacking them with dilute nitri<i
acid they are eaten away until they assume an hour-glass form, and are

^ Read at the Manchester meeting of the British Association, September, 1HH7,

Aotioit of a Magnet on Chbhioal Action

343

furtheimore pitted on the ends in a remarkable manner. On Prof.
Eemsen’s signifying that he had abandoned the field for the present,
Tve set to work to illustrate the matter in another manner by means
of the electric currents produced from the change in the electrochemical
nature of the points and hollows of the iron.

The first experiments were conducted as follows: Two bits of iron
or steel wire about 1 mm. in diameter and 10 mm. long were imbedded
side by side in insulating material, and each was attached to an insulated
wire. One of them was filed to a sharp point, which was exposed by
cutting away a little of the insulation, while the other was laid bare on
a portion of the side. The connecting wires were laid to a reflecting
galvanometer, and the whole arrangement was placed in a small beaker
held closely between the poles of a large electromagnet, the iron wires
being in the direction of the lines of force. When there was acid or
any other substance acting upon iron in the beaker, there was always a
deflection of the galvanometer due to the slightly difiEerent action on
the two poles. When the magnet was excited the phenomena were
various. When dilute nitric acid was placed in the beaker and the
magnet excited, there was always a strong throw of the needle at the
moment of making circuit, in the same direction as if the sharp pointed
pole had been replaced by copper and the other by zinc. This throw
did not usually result in a permanent deflection, but the needle slowly
returned toward its starting point and nearly always passed it and
produced a reversed deflection. This latter effect was disregarded for
the time being, and attention was directed to the laws that governed
the apparent ‘ protective throw,’ since the reversal was so long delayed
as to be quite evidently due to after effects and not to the immediate
action of the magnet.

With nitric acid this throw was always present in greater or less
degree, and sometimes remained for some minutes as a temporary
deflection, the time varying from this down to a few seconds. The
throw was independent of direction of current through the magnet, and
apparently varied in amount with the strength of acid and with the
amoxint of deflection due to the original difference between the poles.
This latter fact simply means that the effect produced by the magnet
is more noticeable as the action on the iron becomes freer.

When a pair of little plates exposed in the middle were substitiited
for the wires, or when the exposed point of the latter was filed to a
flat surface, the protective throw disappeared, though it is to be noted
that the deflection often gradually reversed in direction when the ci\r-

Heney a. Rowland

24 : 4 :

rent was sent through the magnet; i. e., only the latter part of the
previous phenomenon appeared under these circumstances.

When the poles^ instead of being placed in the field along the lines
of force, were held firmly perpendicular to them, the protective throw
disappeared completely, though as before there was a slight reverse
after-effect.

Some of Professor Remsen’s experiments on the corrosion of a wire
in strong nitric acid were repeated with the same results as he obtained,
viz.: the wire was eaten away to the general dumb-bell form, though
the protected ends instead of being club-shaped were perceptibly hol-
lowed. When the wire thus exposed was filed to a sharp point the
extreme point was very perfectly protected, while there was a slight
tendency to hollow the sides of the cone, "and the remainder of the
wire was as in the previous experiments. In both cases the bars were
steel and showed near the ends curious corrugations, the metal being
left here and there in sharp ridges and points. In one case the cylinder
was eaten away on sides and ends so that a ridge -of almost knife-like
sharpness was left projecting from the periphery of the ends.

These were the principal phenomena observed with nitric acid.
Since this acid is the only one which attacks iron freely in the cold, in
Prof. Remsen^s experiment, this was the one to which experiments were
in the main confined. With the present method, however, it was pos-
sible to trace the effect of the magnet whenever there was the slightest
action on the iron, and consequently a large number of substances, some
of which hardly produce any a^on, could be used with not a little facsility.

In thus extending the experiments some difl&culties had to bo
encountered. In many cases the action on the iron was so irregular
that it was only after numerous experiments under widely varying
conditions that the effect of the magnet could be definitely determined.
Frequently the direction of the original action would be reversed in tbo
course of a series of experiments without any apparent cause, but in
such case the direction of the effect due to the magnet remained always
unchanged, uniformly showing protection of the point so long as the
wires remained parallel to the lines of force. When, however, the
original action and the magnetic effect coincided in direction, the repe-
tition of the latter showed a decided tendency to increase the former.

When using solutions of various salts more or less freely precipital:(*d
by the iron, it frequently happened that the normal protective throw
was nearly or quite absent, but showed itself when the magnet circuit
was broken as a violent throw in the reverse direction, showing that the
combination had been acting like a miniature storage battery which

Action of a Magnet on Chemical Action

245

promptly discharged itself when the charging was discontinued by
breaking the current through the magnet. The gradual reversal of
the current some little time after exciting the magnet was noted fre-
quently in these cases, as before. Owing to this peculiarity and their
generally very irregular action, the various salts were disagreeable sub-
stances to experiment with, though as a rule they gave positive results.

Unless the poles were kept clean experimenting became difficult from
the accumulation of decomposition products about them and oxidation
of their surfaces. A few experiments showed how easily the original
deflection could be modified, nearly annulled or even reversed in direc-
tion by slight differences in the condition of the poles. These difficul-
ties of the method are, however, more than counterbalanced by its
vai)idity and delicacy when proper precautions are taken.

Nearly thirty substances were tested in the manner previously de-
scribed; but comparatively few of them gave very decided effects with
the magnet, though, as later experiments have shown, the protective
action is a general one. The substances first tried were as follows.
The table shows the various acids and salts tried, and their effects as
shown by the original apparatus:

Substances.

Effect duo to
Mafrnet.

Notes.

Nitric acid....
Sulphuric ** ....
Hydrochloric acid

Acetic «

Formic “

Oxalic **

Tartaric »

Chromic “

Perchloric “

Chloric “

Bromic

Phosphoric <<

Permanganic “

Chlorine water

Bromine “

Iodine **

Copper sulphate

nitrate

acetate

chloride

tartrate

Mercuric bromide

** chloride

Mercurous nitrate

Ferric chloride

Silver nitrate

Platinum tetrachloride. . .

Strong.

Little or none.

(( it

None.

Some effect.

None.

Slight effect.
Decided “

Some.

Slight.

Some.

Decided.

Some.

Always powerful protective throw.
Does not act very readily on the iron.

Sometimes quite distinct throw, irregular.
Much less marked than with chromic.

Hardly any effect on iron.
More than with perchloric.

Mainly showing as throw, on breaking.

tt tt tt

Throw, on breaking.

Very slight solution, weak.

Mainly as throw on breaking. Lbreaking.
Both protective throw, and sometimes on
Action very irregular.

it tt

246

Henet a. Eowland

Several things axe worthy of note in this list. In the first place
those solutions of metallic salts which are precipitated by iron all show
distinct signs of protective action when the current is passed through
the magnet. Of the various acids this is not generally true; only those
show the magnetic effect, which act on iron without the evolution of
hydrogen, and are powerful oxidizing agents. In general, substances
which acted without the evolution of hydrogen gave an effect with the
magnet.

From these experiments it was quite evident that the protective
action, whatever its cause, was more general than at first appeared and
steps were next taken to extend it to the other magnetic metals- Small
bars were made of nickel and cobalt and tried in the same manner as
before. These metals are acted on but very slightly by most acids, and
the range of substances which could be used was therefore very small,
but all the substances which gave the magnetic effects with iron poles
gave a precisely similar, though much smaller effect, whenever they
were capable of acting at all on the nickel and cobalt. This was notably
the case with nitric acid, bromine water, chlorine water, and platinum
tetrachloride, which were the substances acting readily on the metals in
question. Even with these powerful agents, however, the magnetic
action was very much less than with iron, and experimentation on
metals even more weakly magnetic was evidently hopeless.

As a preliminary step toward ascertaining the cause of the magnetic
action and its non-appearance where the active substance evolved hydro-
gen, it now became necessary to discover and if possible •eliminate thc^
cause of the reversal of the current which regularly followed the protec-
tive throw. Experiments soon showed that it could not be ascribed to
accumulation of decomposition products around the electrodes, and
polarization, while it could readily neutralize the original deflection,
could not reverse its direction. Whatever the cause, it was one which
did not act with any great regularity, and it was soon found that stirring
the liquid while the magnet was on, uniEormly produced the effect ob-
served. Since one pole was simply exposed over a small portion of its
side while the other had a sharp projecting point, it was the latter which
was most freely attacked when there were currents in the liquid, whether
these were stirred up artificially or were produced by the change in gal-
vanic action due to the presence of the magnet. When the polos were
placed in fine sand saturated with acid this reversing action was much
diminished, and in fact anything which tended to hinder free circulation
of the liqxiid produced the same effect. Several materials were tried and

Action op a Magnet on Chemical Action 347

of these the most successful was au acidulated gelatine which was
allowed to harden around the poles. In this case the protective throw
was not nearly as large as in the free acid, since the electrodes tended
to become polarized while the gelatine was hardening, and only weakly
acid gelatine would harden at aU; hut the reversing action completely
disappeared, so that, when the magnet was put on, a permanent deflec-
tion was produced instead of a transitory throw.

This point being cleared up attention was next turned to the negative
results obtained with acids which attack iron with evolution of hydro-
gen. The galvanometer was made much more sensitive and removed
from any possible disturbing action due to the magnet; and with these
precautions the original experiments were repeated, it seeming probable
that even if the magnetic effect were virtually annulled by the hydrogen
evolved, some residual effect might be observed.

This residual effect was soon detected, first with hydrobromic acid,
and then with hydrochloric, hydriodic, sulphuric and others. The
strongest observed effect was with hydriodic acid, but as this may pos-
sibly have contained traces of free iodine it may be regarded as some-
what doubtful. The effect in all these cases was very small, and though
now and then suspected in the previous work, could not have been
definitely determined, much less measured.

Some rough measurements were made on the electromotive forces
involved in this class of phenomena by getting the throw of the galvano-
meter for various small ^own values of the E. M. E. The values found
varied greatly, ranging from less than 0-0001 volt in case of the acids
evolving hydrogen, up to 0-08 or 0-03 volts with nitric acid and certain
salts. These were the changes produced by the magnet, while ih.e
initial electromotive forces normally existing between the poles would
be, roughly speaking, from 0-0001 to nearly 0-06 volts, never disappear-
ing and rarely reaching the latter figure.

Prom these experiments it therefore appears that the protective
action of the magnetic field is general, extending to all substances' which
act chemically on the magnetic metals. While this is so, the strongest
effect is obtained with those substances which act without the evolution
of hydrogen. But the series is really quite continuous, perchloric acid
for instance producing but little more effect than hydrobromic, while
this in turn differs less from perchloric than from an acid like acetic.
It seems probable that tho action of the hydrogen evolved is partially
to shield the pole at which it is evolved, and lessen the difference be-
tween the poles produced by the magnet. It probably acts merely

248

Hbnrt a. Eowland

mechanically, for it is to he noted that those acids which evolve a gas
other than hydrogen (perchloric acid,' for instance), which is not ab-
sorbed by the water, tend to produce little magnetic effect compared
with those which act without the evolution of any gas.

As to the actual cause of the protective action exercised by the mag-
netic field, all these experiments go to show that it is quite independent
of the substance acting, with the exception above noted, and is probably
due to the attractive action of the magnet on the magnetic metals
forming the poles subjected to chemical action, as we have before
explained.

In the first place, whenever iron is acted upon chemically in a mag-
netic field those portions of it about which the magnetic force varies
most rapidly are very noticeably protected, and this protection as nearly
as can be judged varies very nearly with the above quantity. Wherever
there is a point there is almost complete protection, and wherever there
is a flat surface, no matter in how strong a field, it is attacked freely.
Whenever in the course of the action there is a point formed, the above
condition is satisfied and protection at once appears. Thus, in the
steel bars experimented on, whenever the acid reached a spot slightly
harder than the surrounding portions it produced a little elevation from
which the lines of force diverged, and still further shielding it produced
a ridge or point, sharp as if cut with a minute chisel. Nickel and
cobalt tend to act like iron, though they are attacked with such difli-
culty that the phenomena are much less strongly marked. With the
non-magnetic metals they are completely absent. Now, turning to the
experiments with the wires connected with a galvanometer, the same
facts appear in a slightly different form.

When the poles were placed perpendicular to the lines of force instead
of parallel to them, the magnet produced no effect whatever, showing,
first, that the effect previously observed depended not merely on the
existence of magnetic force but on its relation to the poles, and, sec-
ondly, that when the poles were so placed as to produce little deflection
of the lines of force the protective effect disappeared.

When the pointed pole was blunted the effect practically disappeared,
the poles remaining parallel to the lines of force, and when plates were
substituted for the wires no effect was produced in any position, show-
ing that the phenomena were not due to the directions of magnetization
but to the nature of the field at the exposed points. In. short, whatever
the shape or arrangement of the exposed surfaces, if at any point or
points the rate of variation of the square of the magnetic force is

Actiok of a Magnet on Chemioal Action 249

peater than elsewhere, sach points wHl be protected, whHe if the force
is sensibly constant over the surfaces exposed there will be no protection
at any point. With all the forms of experimentation tried this law
held without exception. It therefore appears that the particles of
magnetic material on which the chemical action could take place are
governed by the general law of magnetic attraction and are held in
plnoo against choTuical energy precisely as they would be held against
purely mechanical force. To sum up :

When the magnetic metals are exposed to chemical action in a
magnetic field such action is decreased or arrested at any points where
the rate of variation of the s(juare of the magnetic force tends toward
a maximum.

It is quite clear that the above law expresses the facts thus far
obtained, and while in any given case the action of the magnet is often
complicated by subsidiary effects due to currents or by-products, the
mechanical laws of motion of particles in a magnetic field hold here as
elsewhere and cause the chemical action to be confined to those points
where the magnetic force is comparatively uniform.

The effect of currents set up in the liquid during the action of the
magnet cannot be disregarded especially in such experiments as those
of Nichols (this Journal, xxxi, 272, 1886) where the material acted on
was powdered iron and the disturbances produced by the magnet would
be particularly potent. The recent experiments of Colardeau (Journal
de Physique, March, 1887) while perhaps neglecting the question of
direct protection of the poles, have furnished additional proof of the
purely mechanical action of the magnet by reproducing some of the
characteristic phenomena where chemical action was eliminated and
the only forces acting were the ordinary magnetic attractions.

An attempt was made to reverse the magnetic action, i. e. to deposit
iron in a magnetic field and increase its deposition where there was a
sharp pole immediately behind the plate on which the iron was being
deposited. This attempt failed. The action was very irregular and the
results not decisive. The question of stirring effect was also examined.
TTsually stirring the liquid about one pole increased the action on that
pole, but sometimes produced little effect or even decreased it. This
however is in entire agreement with the irregular action sometimes
observed in the case of the after-effect in the original experiments.

An excellent method of experiment is to imbed an iron point in wax
leaving the minute point exposed: imbed a flat plate also in wax and
expose a point in its centre. Place the point opposite to the plate, but

250

HsimT A. Eowland

not too near and place in the liqnid between the poles of a magnet and
attach to the galvanometer as before.

There is a wide field for experiment in the direction indicated above,
for it is certainly very curious that the effect varies so much. If hydro-
gen were as magnetic as iron, of course acids which liberated it would
have no action. But it is useless to theorize blindly without further
experiment; and we are drawn off by other fields of research.

In this Journal for 1886, (1. c.) Professor E. L. Nichols has investi-
gated the action of acids on iron in a magnetic field. He remarks that
the dissolving of iron in a magnetic field is the same as removing it to
an infinite ^stance and hence the amount of heat generated by the
reaction should differ when this takes place within or without the
magnetic field. Had he calculated this amount of heat due to the
work of withdrawing it from the field, he would probably have found
his method of experiment entirely too rough to show the difference, for
it must be very small. He has not given the data, however, for us to
make the calculation. • The results of the experiments were inconclu-
sive as to whether there was greater or less heat generated in the field
than without.

In the same Journal for December, 1887, he describes experiments
on the action of the magnet on the passive state of iron in the magnetic
field. In a note to this paper and in another paper in this J ournal for
April, 1888, he describes an experiment similar to the one in this paper
but without our theory with regard to the action of points. Indeed
he states that the ends of his bars acted like zinc, while the middle was
like platinum, a conclusion directly opposite to ours. The reason of this
difference has been shown in this paper to be probably due to the cur-
rents set up in the liquid by the reaction of the magnet and the electric
currents in the liquid.

In conclusion we may remark that our results differ from Professor
Nichols in this: First, we have given the exact mathematical theory
of the action and have confirmed it by our experiments, having studied
and avoided many sources of error, while Professor Nichols gives no
theory and does not notice the action of points. Secondly, our experi-
ments give a protective action to the points and ends of bars, while
Professor Nichols thinks the reverse holds and that these are more
easily dissolved than unmagnetized iron.

ON THE ELECTROMAGNETIC EFFECT OF CONVECTION-

CURRENTS

Bt IlBNitT A. Rowland and Cast T. Hotohinson
{Philoiophieal Magazint [5], XXVII, 448-460, 1889]

The first to meutioii the probable existence of an effect of this kind
was Faraday, who says If a ball be electrified positively in the
middle of a room and then be moved in any direction, effects will be
produced as if a current in the same direction had existed.” He was
led to this conclusion by reasoning from the lines of force.

Maxwell, writing presumably in 187S or 1873, outlines an experi-
ment, similar to the one now used, for the proof of this effect.

The possibility of the magnetic action of convection-currents occurred
to Professor Rowland in 1868, and is recorded in a note-book of that
date.

In his first experiments, made in Berlin in 1876, Prof. Rowland used
a horizontal hard rubber disk, coated on both sides with gold, and
revolving between two glass condenser-plates. Each coating of the
disk formed a condenser with the side of the glass nearer it; the two
sides of the disk were charged to the same potential. The needle was
placed perpendicular to a radius, above the upper condenser-plate, and
nearly over the edge of the disk. The diameter of the hard rubber
disk was 21 cm., and the speed 61 per second.

The needle system was entirely protected from direct electrostatic
effect. On reversing the electrification, deflexions of from 6 to 7-5
mm. were obtained, after all precautions had been taken to guard
against possible errors. Measurements were made, and the deflexions
as calculated and observed agreed quite well; but it was not possible to
make the measurements with as great accuracy as was desired, and
hence the present experiment.

Helmholtz,’ in 1876 and later, carried out some experiments bearing

I Experimental ResearoUes, toI. 1, art. 1044.

Abi. 1, p. 778.

252

Henkt a. Sowland

on this subject. According to the potential theory ” of electrody-
namics which he wished to test^ unclosed circuits existed. The end of
one of these open circuits would exert an action on a close magnetic or
electric circuit. So the following experiment was made by M. Schilhu’,"
imder his direction.

A closed steel riag was uniformly magnetized, the magnetic axis coin-
ciding with the mean circle of the ring. This was hung by a long fibre
and placed in a closed metal case. A point attached to a Holtz machine
was fixed near the box, and a brush-discharge was kept up from this
point. If the point acted as a current-end, a deflexion would bo ex-
pected, on the potential theory. No deflexion was observed, although
the calculated deflexion was 23 scale-divisions. The inference is that
either the potential theory is untrue, or else that there is no unclosed
circuit in this case, i. e. that the convection-currents completing the
circuit have an electromagnetic effect.

Schiller’s further work, not bearing directly npon convection-cur-
rents, leads him to the conclusion that all circuits are closed, and that
displacement-currents have an electromagnetic effect.

Dr. Lecher is reported to have repeated Professor Rowland’s experi-
ment, with negative results. His paper has not been found.

Rontgen* has discovered a similar action; he rotates a dielectric disk
between the enlarged plates of a horizontal condenser and gets a de-
flexion of his needle. He apparently guards against the possibility of
this being due to a charge on his disk. A calculation of the force he
measures shows it to he alniost one-eighth of that in the Berlin experi-
ment. His apparatus is not symmetrically arranged, the disk being
mneh closer to the npper condenser-plate; the distances from the upper
and lower plates are 0*14 and 0*26 cm. respectively. Ho usijs a
difference of potential corresponding to a spark-length of 0*3 cm,
in air between balls of 2 cm. diameter, i. e. about 33 oh^ctrostutie
units, equal to the sparking potential between plane surfaces at 0*2(5
cm. The disk is an imperfect conductor, and altogether it doos not
seem clear, in spite of the precautions taken, that this is not dwe to
convection-currents.

In the Berlin apparatns, as stated above, the needle is near the edge
of the disk; the magnetic effect produced is assumed to be proportional
to the surface-density mnltiplied by the linear velocity; hence the force
will he much greater at the edge of the disk than near the centre; but

* cllx, p. 456.

*Sitzb. a, Berl. Akad., Jan, 19, 1888.

Plate V

Eliscteomagnetio Effect of CoNTEOTioisr-CuEEENTS 253

the held will be more iitegiilar, and so make accurate measurements
more difficult.

In the present apparatus a xiniform field is secured by naiTig two
vertical disks rotating about horizontal axes in the same line; the needle
system is placed between the disks, opposite their centres. The disks
are in the meridian; they are gilded on the faces turned towards the
needle. Between the disks are placed two glass condenser-plates gilded
on the surfaces near the disk; and between these glasses is the needle.
The whole apparatus is symmetrical about the lower needle of the
astatic system.

Each disk is surrounded by a gilded hard rubber guard-plate in order
to keep the density of the charge uniform at the edges. The guard-
plates are provided with adjusting-screws to enable them to be put
accurately in the plane of the disks; and the glass plates in turn have'
adjusting-screws for securing parallelism with the guard-plates. The
glass was carefully chosen as being nearly plane. Disks, glass plates,
and guard-plates all have radial scratches, to prevent conduction-cur-
I'cnts from circulating around the coatings.

In the periphery of the disk are set eight brass studs which pene-
trate radially for about 6 centim., then turning off at a right angle run
parallel to the axis until they come out on the surface of the disks.
They there make contact with the gold foil. Metal brushes set in the
guard-plate bear on these studs, and in this way the disks are electrified.

The figure (PI. V, iig. 1) gives a vertical projection of the entire
disk-apparatus : — D T) are the disks; OGQO the guard-rings; YTYT
the condenser-plates ; RRBB hard rubber rings fitting on the should-
ers A A; X X X X bearing-boxes for the axle; P P P P supporting-
standards; PR metal bases sliding in the bed B B, and held in any
position by screws Z; F F the bases carrying the glass plates, sliding in
the same way as the others. 8 8 S 8 are the adjusting-screws for the
guard-plates, and 1 1 for the glass plates. LLLL&ve collars for catch-
ing the oil from the bearings; 0 0, O' O' are speed-counters, 0 0 gear
with the axle, and O' O' with 0 0m the manner shown; each has 200
teeth, and speed-reading is taken every 40,000 revolutions.

The needle system is enclosed in the brass tube T, ending in the
lai’ger cylindrical box in which are the mirror and upper needle. This
is closed in by the conical mouth-piece Q, across the opening of which
is iilacod^n wire grating. The mirror is shown at M, the upper needle
at X' and the lower at N. The system is hung by a fibre-suspension
about 30 cm. in length, protected by a glass tube. The needle-

Hbnky a. Rowland

254:

system is made by fitting two small square blocks of wood on an alumi-
nium wire; on two sides of each of the wooden blocks are cemented
small scraps of highly magnetized watch-spring. The needle thus made
is about 1 X 1 X 10 mm.

The mirror is fixed just below the upper needle, and is read by a
telescope 200 cm. distant. The plane of the mirror is at an angle
of 46® with the plane of the disks for convenience. The whole is sup-
ported by the board 00 attached to a wall-bracket.

Two controlling magnets (W W) with their poles turned in opposite
directions are used. By means of the up and down motion of either
magnet, any change in the sensitiveness can be attained; and by the
motion in azimuth, the zero point is controlled. The advantage of its
use lies in the extremely delicate means it affords of changing the
sensitiveness, much more delicate than with a single magnet.

The bed-plate JB is screwed to one end of a table, at the other end of
which a countershaft is placed (Fig. 2). This is run by an electric
motor in the next room, the belt running through the open doorway.
The motor is 14 metres from the needle.

Although the disks and countershaft were carefully balanced when
first set up, and the table braced and weighted by a heavy stone slab,
yet at the speed used, 125 per second, the shaking of the entire appar-
atus was considerable; the needle was so unsteady that it could not be
read. This was seen to be due to vibrations of the telescope itself and
not to the needle. To prevent it, each leg of the table on which the
telescope rested was set in a box about 30 cm. deep filled with saw-
dust, and a heavy stone slab was placed on top of this table. This
entirely did away with the trouble; the swing of the needle was as
regular when the apparatus was revolving as when it was at rest.

The two hard rubber rings (jBjB) mentioned above have grooves cut
in their peripheries; in these grooves wires are wound. These serve as
a galvanometer for determining the needle-constant. When not in use
they are held in the position shown in the figure, but when it is desired
to determine the needle-constant they are slipped on the shoulders
(AAAA) and pushed up in contact with the back of the disks. Each
has two turns: this arrangement will be referred to as the disk-
galvanometer.

If a known current is sent through the disk-galvanometer, and the
geometrical constant be known, the part of the constant depending on
the field and needle is determined.

The current is measured by a sine-galvanometer, placed in another

Eleotsomaqn’etio Eppeot op Oontbotiokt-Cuebents

2od

part of tlie room. To determine H at the sine-galvanometer a metre
brass circle is put around the sine-galvanometer, and the needle of the
hitter used as the needle of the tangent-galvanometer thus made.
Using this tangcnt-glavanometer in connection with a Weber electro-
dynamometer, Jf at the sine-galvanometer is measured.

The charging was by a Holtz machine connected to a battery of six
gallon Leyden jars. These latter are in circuit with a reversing-key,
an electrostatic gauge, and the disks.

The potential was measured by a large absolute electrometer; all
previous observers have used spark-length between balls, with Thom-
son’s formula. Q-reater accuracy is claimed for this work, largely on
this account.

In this instrument the movable plate is at one end of a balance-arm,
from the other end of which hangs, on knife-edges, a balance-pan.
This movable plate is surrounded by a guard-ring.

The lower plate is fixed by an insulating rod to a metal stem, which
slides up and down in guides. The distances are read off on a scale on
the metal stem. The zero reading is got by inserting a piece of plane
parallel glass whose thickness has been measured. The lower plate and
guard-ring have a diameter of S.*) cm., and the movable disk a diameter
of 10 cm.

The routine of the observations was as follows: — A determination
of n and the needle-constant {P) was first made. The electrostatic
gauge was then set at a certain point,^ and readings of difference of
potential were taken. The disks were now started, electrified, and a
series of three elongations of the needle taken; the electrification re-
versed and three more elongations taken, &c.

About every five minutes speed-readings had to be noted, and at each
reversal it was necessary to replenish the charge in order to keep the
gauge-arm just at the mark. In this way a ‘ series ’ of readings con-
sisting of about reversals was made. After the series, electrometer
readings were again taken; the conditions were then changed in some
way, and another series begun.

The circumstances to be changed are: — distance of disks from needle;
distance of glass plates from needle; electrification; and direction of
rotation.

The calculation of the deflexion is based on the assumption that the
magnetic effect of a rotating charge is proportional to the quantity of
electricity passing any point per second, just as with a conduction-
current. Below are the formula used.

256

Henry A. Eowland

In the equations the letters have the following meanings. All quan-
tities' are given in terms of C. G. S. units.

X = Distance from centre of disk to lower needle.

T = Distance from centre of disk to upper needle,
c =Eadius of disk.

I = Distance between needles.
a = Eadius of windings of disk-galvanometer.

5 = Distance, centre of disk-galvanometer to lower needle.
p =z= Distance, centre of disk-galvanometer to upper needle.

IV = Number of revolutions per second.
a = Surface-density of electrification in electrostatic measure.
F=Eatio of the units.

a = Angle of torsion of the electro-dynamometer.

(p = Angle of deflexion of sine-galvanometer.

8 = Angle of deflexion of tangent-galvanometer.

A = Change of zero-point on electrifying the disks = half the charge
on reversing.

= Scale-reading for disk-galvanometer.
w = Weight on pan of electrometer.

D = Distance of glass plates and disks.
e = Electrometer reading.

X = Condenser distance.

Force, in the direction of the axis, due to a circular current of radius
c, at a distance x on the axis

= ^’'^(c»+ar')j-

Strength of conveetion-curreiit

.% total force due to the disk of radius e

= 471 :*

m /*'

~Vj» (c’+a?)*'

(?dc

and for the two disks acting in the same direction, total force

X=8:r> A .

This gives the force on the lower needle.

BlEOTEOMAGNETIO BeEEOT 01 CONTEOTION-CUEBBNTS 257

Correction for the upper needle:

Potential at any point due to a circular current,

F'= J* Idas;

as equals the solid angle subtended at the point hy the circle

•••

Substituting the value of I, we have as the potential of the disk

But

and

The force
= -dV

p-c_y y/iy

-,=2.

— /.s f / v+1 1.3... (%i — 1) 2i [ c? V* D ■) .

and for the two,

.X.=8<'^[,P.(«)--J;.|P.(«)V...],

where the sign of the entire expression has been changed, since the
poles of the upper and lower needles are opposite.

358

Hbnbt a. Bcwlaitd

Needle — oonetamt.

The disk-galTaiiometer windings have in the same way, for the lower
needle, the force dne to cnrrent I in one turn

= %kIO.

Nor the four turns,

X'=8ffZi7.

Upper needle . — ^The force is got in the same way as for the disk, omit-
ting the integration, i. e. we must multiply the general term of B by

and. replace 2* ^ by I. This gives

a replacing and p^r.

For the total force.

X[ = %7:ID.

Forces acting on the needle system: —

Let M = moment of lower needle,

Let Jf' = moment of upper needle,

then

Couple on lower needle due to field = MM sin
Couple on upper needle due to field = — jET'Jf' sin^.
Total couple = (31^ — M^M*) sin B.

Due to disk-galvanometer:

Couple on lower needle =MX' cos
Couple on upper needle = Jf'X/ cos^.

Total couple = { MX' -i- M'X^' }cos 6,

= S 7 rI{MG-^M'D\QOS 3.

for equilibrium,

SivI{MO + M'D\ cos 6 = H'M'\ sin 3,

, (gJIf- M'M') tan 0

ElBOTROMAGNETIO EbBEOT OB CONVEOTION-CURRBNTS

But ^ = 0*03 nearly, and ^ is approximately unity.

Similarly, for the revolving disks,

= y9 tan J.

. T7 A + J5

•• T'-iO-

For the sme-galTanometer:

/=:p8in f.

r=1831.

and

.% 7= 10^ 5‘46 if sin

/9 = 10-*. 5-46 if sin f>.

tan 0 ^

For measnrenaent of H : —

Electrodynamometer,

*=5'-^ V sma.

g = constant of windings = 10“*. 6*464.
R = moment of inertia = 10“. 8*366.
T = time of one swing = 3*441.

.*. i = 10“®. 7*69 y'sina.

Tangent galvanometer : —

i—^ tan S = -^* tan ft .

G 37r«

n = no. turns = 10.

J = radius turns = 49*98,

.*. i = 0*796 H tan ft,
and, substituting the value of i,

IT — ir>-i Q.KK ^sin o

260

Henet a. Eowland

Surface density {a ): —

<7 is obtained from electrometer-readings.

_ r

A = corrected area of movable plate
= iTc lE'+TJi*-!- . . .}= In { 61 - 01 }.

F=10Xl-’?66i>

and <r = 1-397 -

As soon as the attempt was made to electrify the apparatus, diffi-
culties of insulation were met with. The charged system was quite
extensive, and the opportunity for leakage was abundant; in addition,
the winter here has been very damp. Most of the trouble of this kind*
has been due to the glass in the apparatus ; in no case where glass was
used as an insulator has it proved satisfactory, not even when the air
was dry. First, the stand with glass legs, on which the Leyden-jar
battery was placed, was found to furnish an excellent earth-connection.

Paraffin blocks interposed stopped this. The reversing-key had
three glass rods in it, all of which were found to leak; six different spec-
imens of glass, some bought particularly for this as insulating glass,
were all found to allow great leakage. Shellacing had no effect. Hard
rubber was finally substituted for glass ; and after that the key insulated
very well, even in damp weather.

On charging the glass plates, the disks being earthed, it seemed
almost as if there was a direct earth-connection, so rapid was the fall of
the charge. This was not regarded at the time, as the plates wore
always kept earthed; but later, when it became necessary to charge the
plates, the insulation had to be made good.

Investigation showed that this was caused by leakage directly through
the substance of the glass to the brass back-pieces {H H). Hard rubber
pieces were substituted, and the trouble was entirely removed.

There was at first a deflexion in reversing the electrification while
the disks were at rest. This was of course due to direct electrostatic
effect; but it was not for some time clear where the point of weakness
in the electrostatic screen lay. It was found to be the faulty contact
between the tinfoil covering of the glass tube and the brass collar; the
brass had been lacquered. After this was corrected there was never

BlECTBOMAGNETIO EpPEOT op CONVEOTIOIsr-CURRENTS

^61

again any deflexion on reversing the charge, although the precaution
was taken of testing it every day or so.

The currents induced in the axle by the rotation caused no incon-
venience; if the disks are rotated in the same direction their effect is
added, while the effect of the axles is in opposite directions. Even
when the disks were rotated oppositely, the deflexion due to the axles
was only 3 or 4 cm., and remained perfectly constant.

On running the disks, unelectrified, without the glass plates between
them and the needle, a deflexion of 4 or 5 cm. was noticed. This was
perfectly steady deflexion, and could easily be shown to be due to the
presence of the plate, as it ceased when the plates were replaced.

This was very troublesome for a time, especially as the presence of a
brass plate in place of the glass was found to diminish the deflexion,
but did not bring the needle back to zero as the glasses did. On look-
ing at the figure (Plate V, Fig. 1) it will be seen that there is a brass
plug (7) closing the bottom of the tube in which the needle is placed.
The rapid rotation of the disks caused a very appreciable exhaustion
at the centre, and consequently a steady stream of air was sucked down
the tube through the open mouthpiece, and out through the imperfect
connection of the plug. Air-currents were not at first suspected, as the
deflexion was so very steady. The brass plate used was smaller than
the glass, and hence did not completely shield the tube.

After the brass back-pieces (E H) had been taken out, and a hard
rubber substituted, it was found that with one direction of rotation the
needle was extremely unsteady; it would run up the scale for several
centimetres, stop suddenly, &c.— evidently a forced vibration. This
was traced to air-currents also. ITow, the air blew into the open mouth
of the cone. The apparatus had been run for some months with this
open, and not the slightest irregularity had been seen. But the hard
rubber pieces were very much larger than the brass ones which were
removed; they filled up the lower space to a greater extent, and deflected
the air upwards more than before, causing the unsteadiness. With the
opposite rotation the air was thrown down instead of up, and conse-
quently did not affect the needle.

The first systematic observations were made in January, 1889, with
the disks charged and plates earthed. The deflexion on reversing was
got without difficulty, and it was in the direction to be expected; that
is, with positive electrification, the effect was equivalent to a current in
the direction of motion of the disk. A number of series were taken in
the next two months; they agreed among themselves well enough, but

262

Henry A. Eowland

did not follow the law assumed. The deviation can best be explained
in this way: — ^The equations above show that for a fixed position of

the disks A oc If then, H and ^ being constant, the con-

denser plates are moved np to the disk, step by step, thus varying s,
and D be changed at the same time so as to keep Dle cca^ a constant,
the deflexions should be constant.

Such was not found to be the case; the deflexions were directly
proportioned to e instead of being constant: that is, with greater differ-
ence of potential, the deflexions were greater, although the surface
density remained constant. Finally this was found tp be due to a
charge on the back surface of the gold coating. The end of the axle
comes nearly up to the surface of the disk and taken with all the brass
work must form a condenser of a certain capacity with the inner face
of the gold foil.

This made a change necessary in the method of working; the disks
had to be earthed and the glasses charged. This was done; but now
the deflexions were found always to be greater with positive rotation
(Zenith, N'orth, Nadir, South) then with negative.

It was considered possible that the brushes might have something
to do with this, so they were taken off. Earth connection with the disk
was made by drilling through to the surface of the disk in the line of
the axle and setting in a screw, which came flush with the surface and
also made contact with the axle; this, however, made no difference, the
deflexions for negative rotation were always smaller.

Table I gives the results of a number of observations. All wore
taken with the plates charged and the disks earthed by means of the
axle.

The meaning of the letters has been given; 1/^is directly propor-
tional to the needle sensitiveness.

The sudden variations in. the values of l//9are due to changes pur-
posely made in the needle.

The last column gives the values of F. This work is not intended
as a determination of F, but the calculation is made merely to show to
what degree of approximation the effect follows the assumed law.

The deflexions are about the same as those obtained in the Berlin
experiments — 5 to 8 mm. on reversing. The force measured then
was 1/50000 E; now it is 1/125000 E, The sensitiveness of the needle
in the two cases was almost the same. In the former experiment a
force of 3 X deflected the needle V of arc; the corresponding num-

BlEOTBOMAGNBIIO BpI'JSOX OB CONTEOIION-CUERBNTS 863

ber now is 2-7 X 10~% slightly more sensitive. The scale distances
wore 110 and 800 cm. respectively. So this experiment gives about

Table 1.

No.

Notation.

O’.

1/^.

2A.

2-54

1-24

122

1-16

1-60. 10»

mig.

5-8

S-42.10 W

2-57

((

126

1*8()

8*11

9-0

8-88

129

1-2.3

2-15

6*94

8-00

—

((

129

1-28

6-5S

8-68

1-21

127

1-21

2*26

5-6

8-74

—

133

1-21

5*7

8-74

130

1-47

8*4

8-10

—

138

1-47

7*8

8-04

1-24

121

1-82

2-22

9*4

2-26

—

180

1-82

7*2

8-16

125

1-26

2-17

7*6

2-70

126

1-26

5*7

8-64

2-85

1*60

126

1-19

2-28

6-5

2-82

—

129

1-19

6*0

3-78

—

125

1-11

2-19

5-85

2-82

1-43

127

1-08

2*85

7*8

2*46

128

1-08

5*4

8*82

—

129

1-08

5*8

8*42

3-22

1*80

123

1-18

2-44

5*1

8-80

—

124

1-18

4*9

8-48

8-19x1010

Table II.

mm.

()*7

5-1

5*1

4-9

0*6

8*9

7*0

5-2

8*0

5-0

5-8

5-2

6*3

4-9

8*0

6-0

8 0

5-0

4*8

4-4

5-9

6-6

6-0

5-0

6*5

5-0

the same scale-deflexion at twice the distance with a force as great.
The agreement between the two is seen to be quite good.

The observations, except Nos. 1, 2, 16, and 18 given above, were takeni

264

Henet a. Eowlaed

in pairs — first one direction of rotation and the other immediately after-
wards, everything except the rotation being kept constant.

The table shows that, in every case except one, the deflexion for
negative rotation is appreciably smaller than the corresponding positive.

The difference is too great to be dne to accidental errors in the read-
ings, as the following table, giving the successive deflexions in the case
of ;5?13 and will show.

There is but one deflexion in;^^^13 as small as the mean of;^^14, and
but one in ^14: as large as the mean of

This is a fair example of the way the deflexions mn. As a further
illustration of this takei^^l7' and;5?18; these two are identical in arrange-
ment, but the direction of rotation is in one case got by crossing the
belts from the countershaft to the disks and leaving the main bolt
straight; in the other the main belt is crossed while the auxiliary belts
are straight. The deflexions are the same. This, too, shows that the
difference cannot be due to any effect of the countershaft. The cause
of this has not yet been explained. The work is to be continued with
this and also with new apparatus, made like the Berlin apparatus, but
with the disk much larger, 30 cm. in diameter; at least double the
speed then obtained will be used. This ought to give deflexions on
reversal of 1*5 to 1-7 cm.

The values of V do not agree so well as might be looked for; but
when, in addition to the numerous difldculties already mentioned, the
smallness of the deflexion is considered, and the possibility of the needle
being affected by currents or magnets in other portions of the labora-
tory, so far away as not to be guarded against, and which might well be
changed between the time of taking the observation and the determin-
ation of the needle-constant, and, finally, that a distubing cause of some
kind is still undoubtedly present, the agreement is seen to be as good
as could justly be expected.

Physical Laboratory, Johns Popkins Vniversity,

April 23 , 1889 .

ITotb, added April 29

There seems to be a misunderstanding in certain quarters as to the
nature of the deflexion obtained in Prof. Rowland's first experiment.
The paper reads : — The swing of the needle on reversing the electri-
fication was about 10 to 15 mm., and therefore the point of equilibrium
was altered 6 to 7-6 mm.” This has been construed to mean that the

Eleotbomagstetic Eeebot oe Conveotion-Ctjebents 265

deflexion was merely a throw, and that no continuous deflexion was
obtained. This is entirely erroneous; there was always a continuous
deflexion. The throw was read merely because the needle was always
more or less unsteady, and better results could be got by seizing a
favorable moment when the needle was quiet and reading the throw,
than by attempting to take the successive elongations, or waiting for
the needle to come to rest. In the experiment described above the
needle was very steady and no such trouble was experienced. On elec-
trifying, the needle would take up a certain position and would remain
there as long as the charge was kept up; on reversal, it would move off
to a new and perfectly definite position about 6 to 7 mm. away, and
remain there, &c. H. A. E.

0. T.H.

Oisr THE EATIO OP THE ELEOTEOMAGHETIC TO THE
ELECTEOSTATIC UNIT OP ELECTEIOITY

Bt Hbnbt a, Rotvland, with the assistance of E. H. Hall and L. B. Flbtoubb

iPhiloBophieal Magazine [6], XXVIII^ 804-815, 1889 ; Americcm Journal of Soienee [8],

XXXVJTI, 289-398, 1889]

The detenmnation described below was made in the laboratory of
the Johns Hopkins University about ten years ago, and was laid aside
for further experiment before publication. The time never arrived to
complete it, and I now seize the opportunity of the publication of a
determination of the ratio by Mr. Rosa in which the same standard
condenser was used, to publish it. Mr. Rosa has used the method of
getting the ratio in terms of a resistance. Ten years ago the absolute
resistance of a wire was a very uncertain quantity and, therefore, I
adopted the method of measuring a quantity of electricity electro-
statically and then, by passing it through a galvanometer, measuring it
electromagnetically.

The method consisted, then, in charging a standard condenser, whose
geometrical form was accurately known, to a given potential as meas-
ured by a very accurate absolute electrometer, and then passing it
through a galvanometer whose constant was accurately known, and
measuring the swing of the needle.

Desoeiptioit of Instruments

Electrometer . — This was a very fine instrument made partly according
to my design by Edelmann, of Munich. As first made, it had many
faults which were, however, corrected here. It is on Thomson's guard
ring principle with the movable plate attached to the arm of a balance
and capable of accurate adjustment. The disc is 10-18 cm. diameter
in an opening of 10-38 cm. and the guard plates about 33-0 cm. diam-
eter. All the surfaces are nickel plated and ground and polished to
optical surfaces and capable of accurate adjustment so that the dis-
tance between the plates can be very accurately determined. The
balance is sensitive to a mg. or less and the exact position of the beam

Eatio of Elbcteomaonetio to Eleotbostatio Unit 267

is read by a hair moving before a scale and observed by a lens in the
manner of Sir Wm. Thomson. The instrument has been tested through-
out its entire range by varying the distances and weights to give the
constant potential of a standard gauge, and found to give relative read-
ings to about 1 in 400 at least. It is constructed throughout in the
most elaborate and careful manner and the working parts are enclosed
in sheet brass to prevent exterior action.

As the balance cannot be in equilibrium by combined weights and
electrostatic forces, it was found best to limit its swing to a mm. on
each side of its normal position. The mean of two readings of the
distance, one to make the hair jump up and the other down, constituted
one reading of the instrument.

The adjustments of the plates parallel to each other and of the
movable plate in the plane of the guard ring could be made to almost
^ mm.

The formula for the difference of potential of the two plates is

xrs

where d is the distance of the plates, wg the absolute force on the
movable plate and A its corrected area. According to Maxwell

A = irjiP+iZ'* - (iy* _ i?)

where It and E' are the radii, of the disc and the opening for it and a
= ‘221 (J?' — iZ). The last correction is only about 1 in 500, and
hence we have, finally,

F=mai vwdji + .

Standard condenser . — This very accurate instrumeiit vras made from
my designs by Mr. Grunow, then of New York, and consisted of one
hollow ball, very accurately turned and nickel plated, in which two balls
of different sizes could be hirng by a silk cord. The balls could be very
accurately adjusted in the centre of the hollow one. Contact was made
by two wires about inch diameter, one of which was protruded
through the outer ball until it touched the inner one; by a suitable
mechanism it was then withdrawn and the second one introduced at
another place to effect the discharge. This could be effected five times
every second. The diameters of the balls have been accurately deter-
mined by weighing in water, and the electrostatic capacities found to be
60-069 and 99-666 c. g. s. units.

A further description is given in Mr. Eosa’s paper.

268

Hbnet a. Eowlaitd

Oalvanometer for Electrical Discharges . — This was very carefully
snlated by paper and then put in hot wax in a vacuum to extract the
moisture and fill the spaces with wax. It had two coils, each of about
70 layers of 80 turns each of ISTo. 36 silk covered copper wire. They
were half again as large as the ordinary coils of a Thomson galvano-
meter. The two coils were fixed on the two sides of a piece of vulcanite
and the needle was surrounded on all sides by a metal box to protect
it from the electrostatic action of the coils. A metal cone was attached
to view the mirror through. The insulation was perfect with the
quickest discharge.

The constant was determined by comparison with the galvanometer
described in this Journal, vol. xv, p. 334. The constant then given has
recently been slightly altered. The values of its constant are

By measurement of its coils 1832-24

By comparison with coils of eleetrodynamometer 1833-67

By comparison with single circle 1832-66

Giving these all equal weights, we have

1832-82

instead of 1833-19 as used before.

The ratio of the new galvanometer constant to this old one was
found by two comparisons to be

10-4167
10-4115 ^

Hence we have

Mean, 10-4141
(? = 19087.

Eleetrodynamometer . — This was almost an exact copy of the instru-
ment described in Maxwell^s treatise on electricity except on a smaller
scale. It was made very accurately of brass and was able to give very
good results when carefully used. The strength of current is given
by the formula

O = — ^ ^ Sin a

where E is the moment of inertia of the suspended coil, t its time of
vibration, a the reading of the head, and C a constant depending on
the number of coils and their form.

Ratio of Eleoteomagnbtio to Euboteostatio Unit 269

lABQE OOILS.

Total number of ■windings 240

Depth of groove -84 cm.

Width of groove -76 cm.

Mean radius of coils 13-741 cm.

Mean distance apart of coils 13-786 cm.

SUSPENDED OOILS.

Total number of -windings 126

Depth of groove -41 cm.

Width of groove -38 cm.

Mean radius 2-760 cm.

Mean distance apart 2-707 cm.

These data give, by Maxwell’s formulse,

0 = 0-006457.

In order to be sure of this constant, I constructed a large tangent
galvanometer with a circle 80 cm. diameter and the earth’s magnetism
was determined many times by passing the current from the electro-
dynamometer through this instrument and also by means of the ordi-
nary method "with magnets. In this way the following values were
found.

Maarnetlo

Bleotrloal

method.

December 16, 1879 . .

-19921

-19934

January 3, 1879

-19940

-19942

February 25, 1879 . .

-19887

-19948

Pobruary 28, 1879 . .

-19903

-19910

March 1, 1879

-19912

-19928

Mean

-19912

-19933

differ only about 1 in

1000 from each other.

Hence we

for 0 :

Prom calculation from coils -006467

Prom tangent galviinometer -006451

Mean -006464 0 . g.s; unite.

The suspension was bifilar and no correction was found necessary for

the torsion of the -wire at the small angles used.

270

Heney a. Bowland

The method adopted for determining the moment of inertia of the
suspended coil was that of passing a tube through its centre and placing
weights at different distances along it. In this way was found

K = 826*6 c. g. 8. units.

The use of the electrodynamometer in the experiment was to determine
the horizontal intensity of the earth^s magnetism at any instant in the
position of the ballistic galvanometer. This method was necessary on
account of the rapid changes of this quantity in an ordinary building ^
and also because a damping magnet, reducing the earth^s field to about
•J- its normal value, was used. For this purpose the ballistic galvano-
meter was set up inside the large circle of 80 cm. diameter, with one
turn of wire and simultaneous readings of the electrodynamometer and.
needle of ballistic galvanometer were made.

Thboet op Expbeimbnt.
We have for the potential

For the magnetic intensity acting on the needle

J3'= sin a

^ tan

For the condenser charge

0 = sin |(l + i.l) = iV

[l “ 2+®*®-]

Whence

m^Wd tany
%nckj jTV' siu a 2 sin }

but =

and 2 Bin J ^ 1^1 — i ^ nearly.

So that finally

2ncV^^ 2Vsina^L J

A = 0; -0011; -0030; -0056; -0090 for 1, 2, 3, 4, 5 discharges as inves-
tigated beloTv.

^ This experiment was completed before the new physical laboratory was finished.

Baiio of Elfoisokag^eiio to Elfoibosiatio Unit 27 L

F — -OOIS for first ball of condenser and -0008 for other, as investi-
gated below.

I = correction for torsion of fibre = 0 as it is eliminated.

« = constant of electrometer = 17-221.

0 = constant of ballistic galvanometer = 19087.

= radius of large circle = 42-105 cm.

» = number of coils on circle = 1.
c = constant of electrodynamometer =-006464.

moment of inertia of coil of electrodynamometer = 826-6.

5 = distance of plane of large circle from needle = 1-27.

O' = capacity of condenser = 60-069 or 29-666.

= distance of mirror from scale = 170-18 cm.
w == weight in pan of balance.
t = time of vibration of suspended coil.

7*= time of vibration of needle of ballistic galvanometer.
j9 = defiection of needle on scale when constant current is passed.
a = reading of head of electrodynamometer when constant purreut
is passed.

8 = swing caused by discharge of condenser.
d = distance of plates of electrometer.

N == number of ^scharges from condenser.

1 = logarithmic decrement of needle.

A = correction due to discharges not taking place in an instant.

The principal correction, requiring investigation is A. Let the posi-
tion and velocity of the needle be represented by

2 ! = ffj sin U and v = nj> cos it, where 5 =

At equal periods of time t„ 2#,. etc., let new impulses be given to
the needle so that the velocity is increased by v, at each of these times.
The equations which will represent the position and velocity of the
needle at any time are, then.

272

Hbnbt a. Eowlakd

between 0 and t, x = a^ sin U v = aj> cos bt

“ and %t, x = a' sin l(t + » = a'4 cos b{t + t')

“ at, and %t, X = a" sin b{t + i") v = ci'b cos b{t + O

At the times 0, t„ at„ etc.^ we must bave

x = 0 v„ = a J)

a„ sin U, = o' sin b(t, + <') v„ + afi cos bt, = a'b cos b(t, + < )

o' sin b(^t, + <') = «" sin b(at, + t") v,flb cos bi^t, + i")

etc. = a"6 cos b{^t, + <")

etc.

Whence we have the following series of equations to determine o', o",
etc., and t", etc.

= a^V + Vj* + cos bt,\ sin b{t, + V) = sinW,

= o'^y 4- + 2»„a'S cos i(2/, — <') ; sin J(2#^ + <") = ^sin J(2/, ■<- V)

a'"*J*=o"’y+t;o’+2«;oo"Jcos5(3<,+t"); sin J(3/, +<"')= ^®sin J(3<,+r')

etc. etc.

When it is small compared with the time of vibration of the magnet,
we have very nearly V — — = —1/^, etc.

a« = 2<(1 + cos W,) = 4^o*Cl “ i

=25ao*(l~2f«J*)

Whence

d ^2a,(l-HKy)

a'" =K(1-4(W,7)

=5^o(l”

Now ^ 0 , a', a", a'" and a*' are the valnes of 3 with 1, 2, 3, 4 and 5
discharges and 2ao, 3ao, 4(Xo and 6ao are the values provided the
discharges were simultaneous.

This correction is quite uncertain as the time, is uncertain.

In assuming that the impulses were equal we have not taken account
of the angle at which the needle stands at the second and subsequent
discharges, nor the magnetism induced in the needle under the same
circumstances. One would diminish and the other would increase the

Batio 01* Eleotromagnbtio to Eleotrostatio Uetit 373

effect. I satisjBed myself by suitable experimeuts that the error from
this cause might be neglected.

The method of experiment was as follows: The store of electricity
was contained in a large battery of Leyden jars. This was attached
to the electrometer. The readiug of the potential was taken, the
handle of the discharger was turned and the momentary swing observed
and the potential again measured. The mean of the potentials ob-
served, with a slight correction, was taken as the potential during the
time of discharge. This correction came from the fact that the first
reading was taken before the connection with the condenser was made.
The first reading is thus too high by the ratio of the capacities of the
condenser and battery and the mean reading by half as much. Hence
we must multiply d by 1 — F where F= -0013 for first ball of con-
denser and '0008 for other. This will be the same for 1 or 5 dis-
charges. From 10 to 30 observations of this sort constituted a set, and

the moan value of which was calculated for each observation sepa-
rately, was taken as the res^ilt of the series.

Before and after each series the times of vibration, t and T, and the
readings, f) and a, were taken. The logarithmic decrement was ob-
served almost daily.

Besttlts

The table on the following page gives the results of all the observa-
tions.

These results can be separated according to the number of discharges
as follows :

300-69

298-37

296-73

296-43

296-60

300-17

298-61

296-40

297-24

296-37

396-72

297-43

298-76

301-82

297-38

297-84

297.78

298-66

295-02

296-87

298-90

298- 67

299- 06

300- 80
296-66

300-19

296-75

295-22

296-31

298-80

298-48

297-26

297 15

296-69

Approximate Talue for correction only.

Eatio ov Eleoteomagnetio to Eleoteostatio Unit 276

In taking the mean, I have ignored the difference in the weights due
to the number of observations, as other errors are so much greater than
those due to estimating the swing of the needle incorrectly.

It will be seen that the series with one discharge is somewhat greater
than with a larger number. This may arise from the xmeertainty of
the correction for the greater number of dischargee, and I think it is
best to weight them inversely as this number. As the first series has,
also, nearly twice the nxmiber of any other, I have weighted them as
follows:

Wt. vXlO-'

8 298-80

4 298-48

3 297-26

2 297-15

1 296-69

Mean 298-15

Or « = 2981 5000000 cm. per second.

It is impossible to estimate the weight of this determination. It is
slightly smaller than the velocity of light, but still so near to it that
the difference may well bo duo to errors of experiment. Indeed the
difference amounts to a little more than half of one per cent. It is seen
that there is a systematic falling off in the value of the ratio. This is
the reason of my delaying the publication for ten years.

Had the correction. A, for the number of discharges been omitted,
this difference would have vanished; but the correction seems perfectly
certain, and I see no cause for omitting it. Indeed I have failed to find
any sufficient caxise for this pecxdiarity which may, after all, be acci-
dental.

As one of the most accurate determinations by the direct method and
made with very elaborate apparatus, I think, however, it may possess
some interest for the scientific world.

NOTES ON THE THEORY OF THE TRANSFORMER

iJohm Hiiphim UnivwBity Oireulars^ Jfo. 99, pp. 104, 106, 1892; Philosophical
Magazine L61, XXXIV, 54-67, 1892; XUetHcal World, XX, 20, 1892]

As ordinarily treated the coeflSicient of self and mutual induction of
transformers is assumed to be a constant and many false conclusions
are thus drawn from it.

I propose to treat the theory in general, taking account of the hyster-
esis as well as the variation in the magnetic permeability of the iron.^

The quantity p as used by Maxwell is the number of lines of magnetic
induction enclosed by the given conductor. This will be equal to the
number of turns of the wire into the electric current multiplied by the
magnetic permeability and a constant. But the magnetic permeability
is not a constant but a function of the magrietizing force, and hence we
must write

p = Bny 4* 0(nyy + D{nyy + etc.

Where S, (7, etc., are constants, n is the number of turns and y the
strength of current.

In this series only the odd powers of y can enter in order to express
the fact that reversal of the current produces a negative magnetization
equal in amount to the direct magnetization produced by a direct cur-
rent. This is only approximately true, however, and we shall presently
correct it by the introduction of hysteresis. It is, however, very nearly
true for a succession of electric waves.

To introduce hysteresis, first suppose the current to be alternating so
that y = c sm (it -j- e) where t is the time and e the phase. The intro-
duction of a term A cos (it -}- e) into the value of the number of lines
of induction will then represent the effect very well. But the current
is not in general a simple sine curve and so we must write

y = Oi sin (it + Cl) + 0 ^ sin (2it + ^a) + «* sin (Bit + ^n) + .

^The problem is treated by the method of magnetic circuit first applied by me to
iron bars in my paper on ‘Magnetic Distribution’ (Phil. Mag., 1876), and afterwards
to the magnetic circuit of dynamos at the Electrical Conference at Philadelphia in
1884. I also used the same method in my paper on magnetic permeability in 1878.

Notbs on the Theory oe the Transeormer

277

In this case it is much more diflficiilt to express the hysteresis empir-
ically. In most cases the first term in the value of y is the largest. A
term of the same nature as before will, in this case, suffice to express
the hysteresis approximated. We can then write for the total flux of
magnetic induction

p = -4 cos t7w'y +jDnV+etc.

Problem 1 , — To find the electromotive force necessary to make the
electric current a sine curve in a transformer without secondary. Let
the resistance be R, and make y — CBin (bt). Then Maxwell^s equation
becomes

Substituting the value of y we have

(J2c—Ain) sin (bt^-^Bncb cos (W)+3 sin’(5i) cos W+etc.

But

Sin ^bt cos 5# = -J. (cos U — cos 8 U)

Sin *bt cos S# = (cos 5 — 3 cos 3 W +3 cos U)

Sin *ht cos U = etc.

Hence the electromotive force that must be given to the circuit must
contain not only the given frequency of the current but also frequencies
of 3, 5, 7, etc., times as many. In other words, the odd harmonics.

Problem %. — Transformer without secondary, the electromotive force
being a sine curve.

^sin W = /fy + «

First it is to bo noted that when we place in this equation the general
value of y and make the coefficients of like functions of bt zero, all the
even harmonics will strike out.

Hence the value of the electric current will be

y = (Zj sin (W + Si ) + a, sin (3 bt-\- s,) + a, sin (hbi +■ s,) + .
Substituting this value in the value for p, the equation is theoretically
sufficient to determine a,, a,, etc., and Sj, So, etc. The equations are
cubic or of higher order and the solution can only be approximate and I
have not thought it worth while to go further with the calculation.
However, it is easy to draw the following conclusion:

1. A simple harmonic current through an iron transformer will pro-
duce a secondary electromotive force and current, or both, which con-
tain not only the fundamental period but the higher odd harmonies.

278

Hbnkt a. Eowland

2. TMs effect is not due to hysteresis hut to the variatiou in the mag-
netic permeahility.

3. The harmonics increase with the increase in magnetization of the
iron and nearly vanish as the magnetization decreases, although it is
doubtful if they ever quite vanish. Hence, an increase of resistance
will decrease the harmonics.

4. In the method of introducing the hysteresis into the equations, it
enters as an addition to the resistance in the term Ra^ 4- An6, where
B is the resistance, the maximum current, A the coefiBlcient of hyster-
esis, which is dependent upon the amount of magnetization of the iron,

n the number of turns of wire, and 6 = ^is 2k divided by the time of

a complete period.

The introduction of the hysteresis into the ordinary equations, there-
fore, presents little or no di'fficulty.

Many observers have noted that the current curve in a transformer
was not a sine curve and Prof. Ayrton has shown the presence of the
odd harmonics but gives no explanation. Mr. Fleming has attributed
them to hysteresis, but I believe the present paper gives the first true
explanation.

Problem S , — To find the work of hysteresis. Let the resistance, JB,
be zero. The work done will then be the integral of the current times
the electromotive force, or

the integral to he taken for one period of the current.

w = (bt+e,')y+Bny^^^ +On'S^^j

A TT

w=zA j-ai.

All the other terms are zero.

In a unit of time the energy absorbed is

Aa^

Steinmetz has found by experiment that this varies as the 1*6 power
of the magnetic induction. Of course the present theory gives nothing
of this but only suggests a way of introducing the hysteresis into cal-
culations of this nature. For this purpose replace A by and the

Notes ots the Thbobt of the Tbansfobmbb

379

work of hysteresis hecomes ^ which is thus the fommla of Stem-
metz.

In the case where a secondary exists the number of turns of wire
being and the current y\ we have simply to replace ny in the above
formula by ny + n^-y^ and change the phase of the hysteresis term so
as to be 90* from the combined magnetizing force, ny + nV- The
equations of the currents will then be, by Maxwell’s formula,

+»|

0 = J2y + n‘^.

which suflS.ce to determine both y and y\ The result is too complicated
to be attractive. The eq[uations show, however, that the odd harmonics
must appear in either the electromotive forces or the primary or second-
ary currents, if not in all of them at once. The exact distribution is
only a case of complicated calculation.

It is to be specially noted that all formulse by which self induction is
balanced by a condenser will not be correct when applied to an iron
transformer but only to an air transformer. They will, however, apply
approximately to iron transformers in which the magnetization is small
and thus probably will apply better to transformers with an open
magnetic circuit than with a closed one. ‘

Also an iron transformer should not bo compared with an air trans-
former or two iron transformers with different magnetizations with
each other.

In conclusion I may add that the mathematical difldculties might be
overcome by another mode of attack but other work draws me in
another direction and I leave the matter to be worked up further by
others.

NOTES ON THE EFFECT OF HAEMONICS ON THE TRANS-
MISSION OF POWER BY ALTERNATING CURRENTS

IMeetrical Worlds XZ", 868, 1892; La iMmilre XLYII^ 42-44, 1898]

In a recent nmnber of The Johns Hopkins TJniversity Circular and
tiie Phil. Mag. for July, 1892/ I have shown that an iron transformer
introduces harmonics of the periods 3, 5, 7, etc./ times the fundamental
period into the currents and electromotive forces both primary and
secondary of a transformer and that these increased in value as the
iron was more and more magnetized.

It is my present object to call attention to the effect of these har-
monics on the transmission of power and its measurement. For light-
ing purposes they are evidently of very little significance, as currents
of all periods are equally efiBicient in producing heat. There is a loss,
however, in the fact that they cause more loss of heat in the wires and
the iron of the transformers. But for the transmission of power the
case is very different. Here the motors are designed to run at speeds
dependent on the period; if there is more than one period the adjust-
ment fails, and there is a loss. The harmonics are thus useless in the
transmission of power by synchronous motors, and are of very little use
in motors with revolving fields. In these cases the harmonics travel
around the circuits, heating the wires and the iron without producing
valuable work. They then represent an almost complete loss in the
transmission of power, and as they may contain 10, 20 or even 30 or 40
per cent of the current, according to the magnetization of the trans-
former, they are probably responsible for some loss of efficiency in many
cases, as will be shown further on.

Indeed, I believe they are the explanation of many seeming mysteries
in the working of alternating current motors.

Special arrangements of condensers and coils can be made to pick
out these harmonics so that they become more important than the

iSee also the Electrical World of July 9, 1892.

“The periods 2, 4, 6, etc., can evidently he introduced by magnetizing the iron of
the transformer in one direction by a constant current, or having it originally with
an asymmetrical magnetic set.

Epfbot op Habmonios on the Teansmission op Power 281

original period. This may occur accidentally and cause many curious
results in the working of motors.

It is, then, of the first importance in the transmission of power that
the curves shall he pure sine curves, and dynamos,* transformers and
motors must he designed in the future with reference to this point.
It would seem, also, that most calculations on the eflSiciency of power
transmission hy alternating currents must he at fault unless they
include the action of the harmonics.

As to the amount of loss from this cause it is difficult to decide in
general. With synchronous motors the harmonics simply fiow around
the wires without producing useful current of any kind. But this may
not cause great loss if the resistance is small. Indeed, considerable
distortion may represent small loss of power in certain cases and great
loss in others, according to the difference of phase of the current and
electromotive force in the harmonics.

In the case of motors with rotary fields the harmonics produce fields
revolving with velocities 3, 5, 7, etc., times the primary field. ITow it
is essential for the efficiency of these motors that the armature shall
revolve nearly as fast as the field, and hence the efficiency for the
harmonics must he very small indeed, and this must decrease the effi-
ciency of the apparatus as a whole.

As to the heating of the wires hy the harmonics, it is easy to see that
the total heating due to all the currents of different periods will simply
he the sum of the heatings due to each of the currents separately.

The effect of harmonics on the hysteresis is much more complicated
and can hardly be calculated without further experiment. However,
the following hypotheses may give some idea of the action. Let the
primary electromotive force he considered unity, and let etc., ho
the electromotive forces of the harmonics. If those acted separately
on the hysteresis the total would he:

1+3 +5(-^y‘®+

Again, if they all combined so that the maximum electromotive force
is equal to the stim of them all, the hysteresis will he nearly:

•6

® Dynamos and motors introduce the odd harmonics on account of the variations
of the self-induction of the machine, which becomes very apparent when a strong
current is flowing. The armature reactions may also introduce the harmonics.

Hbnbt a. Rowlaito

Honrever, it is hai^dly probable that this last condition would be often
satisfied, in which case this formula would give too great a value.
When the harmonics are small this last formula can be written nearly

1 + 1-6 ^•^-4- -J- + etc.)

As an example, suppose a^=’S and ^^=*2 and ^7 = 1, these two
foTmnLse give an increase of 10 and 24 per cent in the loss dne to
hysteresis.

The current heating is only

1 + di -h + etc.*

Or, in the example, ■

1 + -09 + -04 -f -01 = 1*14.

It would seem, then, that the losses dne to hysteresis and cnrrent
heating may he much increased by the harmonics.

I believe the statement has been made that the form of the curve
does not influence the hysteresis. This is evidently incorrect, unless
we take the top of the curve to reckon from, in which case the statement
agrees with the second hypothesis given above if the harmonics are of
the proper phase.

To estimate the influence on the efficiency of a plant, assume the
efficiency of the dynamo and synchronous motor with primary currents
as each equal to 90 per cent, and of the two transformers equal to 93
per cent, and assume that all the currents have the same harmonics as
given above. The total efficiency will be 70 per cent. If the harmonics
are now added, the 30 per cent loss will become about 35 per cent, the
efficiency will be decreased to 65 per cent nearly, a loss of 5 per cent.
There is too much assumption about this calculation to warrant full
belief, and the figures are given more as a challenge to further investi-
gation than as facts. That there is a decrease of efficiency is certain,
-but the amount must be determined by further experiment and mathe-
matical investigation. But, however small the. loss, provided it occurs
in the transformers or the dynamos and motors, it may be of great
consequence on account of its heating effect, because the output of
these is limited by the amount of the heat generated.

The practical conclusion seems to be that transformers and the arma-
tures of dynamos to be used in the transmission of power must be
designed for low magnetizations. By experiment with transformers,

^This fornmla asBumes that the resistance Is the same for the harmonics, whereas
it is greater on acconnt of the * skin ' effect.

Effbot of Harmonics on the Transmission of Power 283

made by Dr. Duncan in this laboratory, immense distortion of the
curves has been found when the induction exceeds 12,000 lines per
square centimetre, while the curves are comparatively smooth with only
BOOOj hence I scarcely think it advisable to use more than 6000 for
transformers, even though low frequency were used. As to dynamos
and motors the limit will depend on the variety of machine used and
will not influence the better class very much.

The fixing of the limit of magnetization of transformers at 6000
causes the output with given current to vary inversely as the frequency.
As the hysteresis with slow frequency will be less, we may increase the
current somewhat to make up for it. As to the exact law, it depends
on the relative dimensions of wire and iron. Practically we might
estimate for an ordinary transformer that the output varied inversely
as the eight-tenth power of the frequency.

The law that the output varies inversely as the four-tenth power of
the frequency assumes that the magnetization increases with decrease
of frequency and thus distorts the curves as shown above.

The immense increase of the size and cost of transformers when dis-
tortion of the curve is avoided precludes the use of very low frequencies
oven were it otherwise desirable.

It is to be noted that the action of the iron in producing harmonics
is directly on the electromotive force, and the amount of current flow-
ing will depend on the resistance and the self-induction of the circuit.
The resistance, owing to so-called ‘ skin ’ ofEect, will bo greater for the
harmonics than for the fundamental peidod. Self-induction depending
on the air will always diminish the harmonics, while if it is duo to iron
it may either increase or decrease them according to their phase. ‘

The measurement of the energy supplied by an alternating current is
also much complicated by the presence of harmonics.

Let the current bo

0= sin (It + <p) + A^ sin (3 U -f- ?,) + At sin (6 bt -|- ?-,) +
and electromotive force

B= sin bt + sin (3 bt + <}'^ + Bt sin ( 6 + 4'^ -f-

The energy transmitted is, then, per unit of time

/ OBdt=ll CJE!d(bt)

If n is the number of oom]deto periods in the primary term, then h ==
2nn and the energy transmitted per second becomes

4[A, By cos <9 + A, Bt cos (^9, - V’’,) + At Bt oos («9, — </-,) + etc.]

284

Hbnet a. Bowland

An ordinary wattmeter in the form of an electrodynamometer with
non-inductive coils would give the correct value of this quantity, hut
any attempt to multiply the mean electromotive force by the current
and the cosine of the phase would lead to an incorrect result unless this
was done for each harmonic separately.

It is to be noted that the introduction of condensers to balance self-
induction win only work for one period at a time.

Indeed very many of the results hitherto obtaiued by observers and
theorists will require modification in the presence of these harmonics.

It would seem from the above that the transmission of a current for
electric lighting is quite a different thing from the transmission of a
suitable current for motors. It vriill be remembered that the transmis-
sion in the Frankfort-Lauffen experiment was one of a lighting current
alone and that some mystery seems to hang over the motor tests. Can
the presence of these harmonies have anything to do with this ?

MODERN THEORIES AS TO ELECTRICITY

iTliS JSngineeritig MagcuAm^ F/JJ, 589-696, January, 1896]

It is not uncommon for electricians to be asked wbether modem
science has yet determined the nature of dectricity, and we often find
difficulty in answering the question. When the latter comes from a
person of small knowledge which we know to be of a vague and general
nature, we naturally answer it in an equally vague and general manner j
but when it comes from a student of sdence aimous and able to bear
the truth, we can now answer with certainty that electricity no longer
exists. Electrical phenomena, electrostatic actions, electromagnetic
action, electrical waves, — ^these still exist and require explanation; but
electricity, which, according to the old theory, is a viscous fluid throw-
ing out little amceba-like arms that stick to neighboring light sub-
stances and, contracting, draw them to the electrified body, dectricity
as a self-repellent fluid or as two kinds of fluid, positive and negative,
attracting each other and repelling themsdves, — ^this electricity no
longer exists. For the name electricity, as used up to the present time,
signifies at once that a substance is meant, and there is nothing more
certain to-day than that electricity is not a fluid.

This makes the task of one who attempts to explain modern elec-
trical theory a very difficult one, for the idea of dectricity as a fluid
pervades the whole language of electrical science, and even the defini-
tions of electrical units as adopted by all scientists suggest a fluid theory.
No wonder, then, that some practical men have given up in despair
and finally concluded that the easiest way to understand a telegraph
line is to consider that the earth is a vast reservoir of dectrical fluid,
which is pumped up to the line wire by the battery and Anally descends
to its proper level at the distant end. Is not this the proper conclusion
to draw from that unforttinate term ‘ electric current ' ? Remember-
ing this fact, — ^that we cannot yet free ourselves from these old theories,
and exactly stiit our words to our meaning, — ^we shall now try to under-
stand the modem progress in dectrical theory.

This whole progress is based upon somettog in the human mind
which warns us against the possibility of attraction at a distance

286

Henet a. Eowland

througli vacant space: Newton felt this impossibility in the cash of
gravitation, but it is to Faraday that we must look principally for the
idea that electrical and magnetic actions must be carried on by means
of a medium filling all space and usually called the ether. The develop-
ment of this idea leads to the modern theory of electrical phenomena.

Take an ordinary steel magnet and, like Faraday, cover it with a
sheet of paper, and upon this sprinkle iron filings. Mapped before us
we see Faraday^s lines of magnetic force extending from pole to pole.
We can calculate the form of these lines on the supposition that a
magnetic fluid is either distributed over the poles of the magnet or
on its molecules, assuming that attraction takes place through space
without an intervening medium. But at this idea the mind of Faraday
revolted, and he conceived that these lines, drawn for us by the iron
filings, actually exist in the ether surrounding the magnet; he even
conceived of them as having a tension along their length and a repul-
sion for one another perpendicular to their length.

Two magnets, then, near each other, become connected by these lines,
which, like little elastic bands always pulling along their length, strive
to bring the magnets together. These so-called lines of force (now
called tubes of force) were, by his theory, conducted better by iron and
worse by bismuth than by the ether of space, and so gave the explana-
tion of magnetic attraction and diamagnetic repulsion.

The same theory of lines of force was also applied by Faraday to
electrified bodies, and thus all electrostatic attractions were explained.
By this idea of lines of force it will be seen that Faraday did away
with all action at a distance and with all magnetic and electrical fluids,
and substituted, instead, a system in which the ether surrounding the
magnet or the electrified body became the all-important factor and the
magnet or electrified body became simply the place where the lines of
force ended: where a line of magnetic force ended, there was a portion
of imaginary magnetic fluid; where a line of electric force ended, there
was a portion of imaginary electric fluid. As the quantities of so-
called plus and minus electricity in any system are equal, we can
thus imagine every charged electrical system to be composed of a
group of tubes of electrical force (more strictly electric induction)
which unite the plus and minus electrified bodies, each unit tube having
one unit of plus electricity on one end and one unit of minus electricity
on the other. The tension along the tube explains the reason why
such an arrangement acts as if there were real plus and minus elec-
trical fluids on the ends of the tube, attracting one another at a die-

Modern Theories as to Electricity

287

tance. Consider a plus electrified sphere far away from other bodies.
The lines of force radiate from it in all directions, and, being symmetri-
cal around the sphere, they pull it equally in all directions. ITow
bring near it a minus electrified body, and the lines of force turn toward
it and become concentrated on the side of the sphere toward such a
body. Hence the lines pull more strongly in the direction of the
negative body, and the sphere tends to approach it.

In the case of a conducting body the lines of force always pass out-
wards perpendicularly to the surface, and hence, if we know the distri-
bution of the lines over the surface^ or the so-called surface density of
the electricity, we can always tell in which direction the body tends to
move. It is not necessary to know whether there are any attracting
bodies near the conductor, but only the distribution of the lines. These
lines then do away with all necessity for considering action at a dis-
tance, for we only have to imagine a kind of ether in which lines of
force with given properties can exist, and we have the explanation of
electric attraction.

But the question now arises as to how the lines of electric force can
be produced in the ether, or, in other words, how bodies can be charged.

In the first place we know that equal quantities of plus and minus
electricity are always produced. As an illustration, suppose it is re-
quired to charge two balls with electricity. Pass a conducting wire
between them with a galvanic battery in its circuit. The galvanic
battery generates the lines of force; these crowd together around it and
push each other sideways until their ends are pushed down the wire
and many of them are pushed out upon the balls.

When the tension backwards along the lines of force just balances
the forward push of the electromotive force of the battery, equilibrium
is established. If the wire is a good conductor, there may be electrical
oscillations before the lines come to rest in a given position, and this I
shall consider below.

The motion of the ends of the lines of force over and in the wire
constitutes what is called an electric current in the wire which is
accompanied by magnetic action around it and also by waves of electro-
magnetic disturbance which pass outward into space.

If, after equilibrium is established, we remove the wire, we have
simply two charged spheres connected by lines of electrostatic force
and thereby attracted to each other. If wo replace the battery by a
dynamo or by an electric machine the effect is the same.

But there is another way by which bodies arc often charged and

2SS

Hbnet a. Eowland

that is by friction. In this case we can suppose the glass to take hold
of one end of the lines of force and the rubber the other end and it is
then only necessary to pull the bodies asunder to Sll the space with
lines. The friction is merely needed to bring the two bodies into inti-
mate contact and remove them gently from each other.

The following considerations may guide us in understanding the
details of the process. It is well known from Faraday^s researches
that a given quantity of electricity has a jBxed relation to the chemical
equivalents of substances. Thus it requires 10,000 absolute electro-
magnetic units of electricity to deposit 114 grams of silver, 68 grams of
copper, 34 grams of zinc, etc.

Hence we can consider, for instance, in chloride of silver that the
atoms of silver are joined to the atoms of chlorine by lines of electro-
static force which hold them to each other. If, by rubbing the chloride
of silver, we could remove the chlorine on the rubber while leaving
the silver, we could stretch them asunder and so fill space wiih the lines
of electrostatic force. According to this theory, then, each atom has
a number of lines of force attached to it, and it is only by stretching
the atoms apart that we can fill an appreciable space with them and so
cause electrostatic action at a distance.

We come to the conclusion, then, that all electrification is originally
produced by separating the atoms of bodies from one another, which
can be done by breaking contact, by friction, or by direct chemical
action of one substance on another, or in some other manner not so
common. The lines of electrostatic force iu a case of electricity at
rest must always begiu and end on matter, and they can never have
their ends in space free from matter. The ends can be carried along
with the matter, constituting electric convection, or they can slide
through a metallic conductor or an electrolyte or rarefied gas, making
what we call an electric current; but, as they cannot end in a vacuum,
they cannot pass through, it. Thus we conclude that a vacuum is a
perfect non-conductor of electricity.

The exact process by which the ends of the lines of force pass
through and along a conductor can at present be only dimly imagined,
and no existing theory can be considered as entirely satisfactory. In
the case of an electrolyte, however, we can form a fairly perfect picture
of what takes place as the decomposition goes on. Thus, in the case of
zinc and copper in hydrochloric acid, we can imagine the zinc plate
attracting the chlorine of the acid, thus stretching out the natural line
of electric force connecting the chlorine atom and the first hydrogen

Modebn Thboeies as to Elboteioitx

289

atom; we can imagine the atoms of chloiine and hydrogen in the body
of the liquid recombining with each other and their Unes of force nnit-
ing nntil they form a complete line long enough to stretch from the
zinc to the copper plate; and all without once m airing a line of force
without its end upon matter. We can further imagine the ends of this
line sliding along the copper and zmc plates to the conducting wires
and down their length, thus making an electric current and carrying
the energy of chemical action to a great distance.

If the ends of the lines should slide along the wire without any
resistance, the wire would he a perfect conductor: but all substances
present some resistance, and in this case heat is generated. This we
always find where an electric current passes along a wire: as to the
exact nature of this resistance or the nature of metallic conduction in
general we know little, but I helieTe we are approaching the time when
we can at least imagine what happens in this most interesting case.

Besides the heating due to the electric current, steadily fiowing, we
must now account for the magnetic lines of force surrounding the cur-
rent and the magnetic induction of one current on the other.

If the current is produced by the ends of the tubes of electrostatic
force moving along the wire, then we may imagine that the movement
of the lines of electrostatic force in space produces the lines of mag-
netic force in a direction at right angles to the motion and to the
direction of the lines of electrostatic force. At the same tune we must
be careful not to assume too readily that one is the cause and the other
the effect: for we well know that a moving line of magnetic force (more
properly induction) produces, as Faraday and Maxwell have shown, an
electric force perpendicular to the magnetic line and to the direction of
motion. Neither line can move without being accompanied by the
other, and we can, for the moment, imagine either one as the cause of
the other. However, for steady currents, it is simpler to take the mov-
ing lines of electrostatic force as the cause and the magnetic lines as
the effect.

We have now to consider what happens when we have to deal with
variable currents rather than steady ones.

In this case we know from the calculations of the great Maxwell
and the demonstrations of Hertz that waves of electromagnetic disturb-
ance are given out. To produce these waves, however, very violent
disturbances are necessary. A fan waved gently in the air scarcely
produces the mildest sort of waves, while a bee, with comparatively
small wings moved quickly and vigorously, emits a loud sound.

290

Hbnbt a. Eowland

So, with electricity, we iinist have a very violent electrical vibration
before waves carrying much energy are given out.

Such a vibration we find when a spark passes from one conductor
to another. The electrical system may be small in size, but the im-
mensely rapid vibrations of millions of times per second, like the quick
vibration of a bee^s wing, sends out a volume of waves that a slowly
moving current is not capable of producing. The velocity of these
waves is now known to be very nearly 300,000 kilometers per second.
This is exactly the velocity of waves of light, or other radiation in
general, and there is no doubt at present in the minds of physicists
that these waves of radiation are electromagnetic waves.

By this great discovery, which almost equals in importance that of
gravitation. Maxwell has connected the theories of electricity and of
light, and no theory qf one can be complete without the other. Indeed
they must both rest upon the properties of the same medium which
jfiUs all space — ^the ether.

Not only must this ether account for all ordinary electrical and mag-
netic actions, and for light and other radiation, but it must also account
for the earth^s magnetism and for gravitation.

To account for the earWs magnetism, we must suppose the ether
to have such properties that the rotation of ordinary matter in it pro-
duces magnetism. To account for gravitation it must have such prop-
erties that two masses of matter in it tend to move toward each other
with the known law of force, and without any loss of time in the action
of the force. We know that moving electrical or magnetic bodies re-
quire a time represented by the velocity of light before they can attract
each other in the line joining them. But, for gravitation, no time is
allowable for the propagation of the attraction.

But the problem is not so hopeless as it at first appears. Have we
not in two hundred and fifty years ascended from the idea of a viscous
fluid surrounding the electrified body and protruding arms outward to
draw in the light surrounding bodies to the grand idea of a universal
medium which shall account for electricity, magnetism, light, and

gravitation ? *

The theory of electricity and magnetism reduces itself, then, to th(^
theory of the ether and its connection with ordinary matter, which we
imagine to be always immersed in it. The ether is the modium by
which alone one portion of matter can act upon another portion at a
distance through apparently vacant space.

Let us then attempt to see in greater detail what the ether must
explain in order that we may, if possible, imagine its nature.

Modern Theories as to Elboxeioitt

291

Ist. It must be able to explaiu electrostatic attraction. These
electrostatic forces are mostly rather feeble as we ordinarily see them.
Air breaks down and a spark passes when the tension on the ether
amounts to about pound to the square inch. It is the air, how-
ever, that causes the break-down. Take the air entirely away, and we
then know no limit to this force. In a suitable liquid it may amount
to flOO times that in air or 5 poimds to 1 square inch, and become a
very strong force indeed. In a perfect vacuum the limit is unknown,
but it cannot be loss than in a liquid, and may thus possibly amount
to hundreds, if not thousands, of pounds to the square inch.

2d. It must explain magnetic action. These actions are apparently
stronger than electrostatic actions, but in reality they are not neces-
sarily so. A tension on tlie ether of only a few hundred pounds on
the square inch will account for all magnetic attraction that we know of,
although we are able to fix no limit to the force the ether will sustain.
No signs have ever been discovered of the ether breaking down.

Again, we must be able to account for the magnetic rotation of
polarized light as it passes through the magnetic field; and it can only
be accounted for by assuming a rotation around the lines of mag-
netic force. This action, however, takes place only while the lines
of magnetic force pass throiigh matter, and it has never been observed
in the ether itself. The velocity of rotation, however, is immense, the
piano of polarization rotating in some cases 800,000,000 times per
second.

The ether must also account for the earth’s magnetism. If we
assume that magnetic lines of force are simply vortex filaments in the
ether, wo have only to suppose that the ether is carried around by the
rotation of the earth, and we have the explanation needed. The mag-
netism of the earth would then be simply a whirlpool in the ether.

8d. The ether must bo able to transmit to a distance an immense
amount of energy either by moans of electromagnetic waves as in light
or by the similar action which takes place in the ether surrounding- a
wire carrying an electric current.

The amount of energy which can be transmitted by the ether in
this manner is enormous, far exceeding that which can be carried by
anything composed of ordinary matter. Thus take the case of sun-
light: on the earth’s surface illuminated by strong sunlight a horse-
power of energy falls on every 7 square feet. At the surface of the
sun the etherial waves carry energy outward at the rate of nearly 8000
horse-power per square foot I

Hbnet a. Eowland

Again, an electric we as large as a knitting needle, surrounded
witk a tube half an inch in diameter in which a perfect vacuum has
been made to prevent the escape of electriciiy, may convey to a dis-
tance a thousand horse-power, indeed even ten thousand or more horse-
power, there being apparently no limit to the amount the ether can
carry.

Compare this with the steam-engine, whore only a few hundred
horse-power require an miormous and clumsy steam pipe. Or, again,
the amount carried by a steel shaft, which, at ordinary rate of speed,
would require to be about a foot in diameter to transmit 10,000 horse-
power.

when we compare the energy transmitted through a square foot of
ether in waves, as in the case of the sun, with the amount that can be
conveyed by means of sound waves tu air or even sound waves in steel,
the comparison becomes simply ridiculous, the ether being so im-
mensely superior. As quick as light, the ether sends its wave energy
to the distance of a million miles while the sluggard air carries it one.
Thus, with equal strain on each, the other carries away a million tltncjs
the energy that the air could do.

4th. The ether must account for gravitation. For this purpose we
are allowed no time whatever to transmit the attraction. As soon as
the position of two bodies is altered, just so soon must the lino of action
from one to the other bo in the straight lino between them.

If this were not so, the motion of the planets around the sun would
be greatly altered. Toward the invemtion of such an other, capable
of carrying on all these actions at once, the minds of many scientific
men are bent. FTow and then wo are able to give the ether such proper-
ties as to explain one or two of the phenomena, but we always come
into conflict with other phenomena that equally demand explanation.

There is one trouble about the other which is rather difficult to
explain, and that is the fact that it does not seem to concentrate itself
about the heavenly bodies. As far as wo are able to test the point,
light passes in a straight line through space oven when near one of
the larger planets, unless the latter possesses an atmosphere. This
could hardly happen unless the ether was entirely incompressible or
else possessed no weight.

If the ether is the caiiise of gravitation, however, it is placed out-
side the category of ordinary matter, and it may thus have no weight
although still having inertia, — a thing impossible for ordinary matter
where the weight is always exactly proportional to inertia.

MODBEIT THEOBIHS ±S TO BlBOXEIOITT

293

Ether, then, is not matter, but something on which many of the
properties of matter depend.

It is curious to note that Newton conceived of a theory of gravita-
tion based on the ether, which he supposed to be more rare around
ordinary matter than in free space. But the above considerations
would cause the rejection of such a theory. We have absolutely no
adequate theory of gravitation as produced by ether.

To explain magnetism, physicists usually look to some rotation in
the ether. The magnetic rotation of the plane of polarization of light
together with the fact of the mere rotation of ordinary matter, as
exemplified by the earth^s magnetism, both point to rotation m the
ether as the cause of magnetism. A smoke ring gives, to some extent,
the modem idea of a magnetic line of force. It is a vortex filament
in the ether.

Electrostatic action is more difficult to explain, and we have hardly
got further than the vague idea that it is due to some sort of elastic
yielding in the ether.

Light and radiation in general are explained when we understand
clearly magnetic and electrostatic actions as the two are linked together
with certainty by MaxweU^s theory.

Where is the genius who will give us an ether that will reconcile
all these phenomena with one another and show that they all come
from the properties of one simple fluid filling all space, the life-blood
of the universe — ^the ether?

ELECTEICAL MEASTJBEMENT BY ALTEEKATING CTTEEENTS

iAmerican Journal of Science [4], IV, 429-448, 1897 ; Philosophical Magazine [5], XL V,

66-86, 1898]

The electrical quantities pertaining to an electric current which it
is usually necessary to measure, outside of current, electromotive force,
watts, etc., axe resistances, self and mutual inductances and capacities.
I propose to treat of the measurement of alternating currents, electro-
motive force and watts in a separate paper. Eesistances are ordinarily
best dealt with hy continuous currents, except liquid resistances. I
propose to treat in this paper, however, mainly of inductances, self and
mutual, and of capacities together with their ratios and values in abso-
lute measure as obtained by alternating currents. I also give a few
methods of resistance measurement more accurate than usually given
by means of telephones or electrodynamometers as usually used and
specially suitable for resistances of electrolytic liquids.

I have introduced many new and some old methods, depending upon
making the whole current through a given branch circuit equal to zero.
These always require two adjustments and they must often be made
simultaneously. However, some of them admit of the adjustments
being made independently of each other, and these, of course, are the
most convenient. But all these zero methods do not admit of any
great accuracy unless very heavy currents are passed through the
resistances. The reason of this is that an electrodynamometer cannot
be made nearly as sensitive for small currents as a magnetic galvano-
meter. The deflection of an electrodynamometer is as the square of
the current. To make it doubly sensitive requires double the number
of turns in loth the coils. Hence we quickly reach a limit of sensitive-
ness. It is easy to measure an alternating current of -0001 ampere and
difficult for *00001 ampere, A telephone is more sensitive and an
instrument made by suspending a piece of soft iron at an angle oC 45®,
as invented by Lord Eayleigh, is also probably more sensitive.

For this reason I have introduced here many new methods, depend-
ing upon adjusting two currents to a phase-difference of 90® which I
believe to be a new principle. This I do by passing one current through

ELEOTBIOAL MbASTJEEMENT BT ALTBENATIN-a CtTEEBNTS 395

the fixed and the other through the suspended coil of an electrodynamo-
mcter. By this means a heavy current can he passed through the fixed
coils and a minute current through the movable coil, thus multiplying
the sensitiveness possibly 1000 times over the zero current method.

I have also found that many of the methods become very simple if
wo use mutual inductances made of wires twisted together and wound
into coils. In this way the self inductances of the coils are aU practi-
cally equal and the mutual inductances of pairs of coils also equal.
Hence we have only to measure the minute diflerrace of these two to
reduce the constants of the coil to one constant, and yet by proper
connections we can vary the inductances in many ratios. Three wires
is a good number to use. However, the electrostatic induction between
the wires must be carefully allowed for or corrected if much greater
accriracy than is desired.

By these various methods the measurement of capacities and induc-
tances has been made as easy as the measurement of resistances, while
the accuracy has been vastly improved and many sources of error
suggested.

Relative results are more accurate than absolute as the period of an
alternating current is difficult to determine, and its wave form may
depart from a true sine curve.

Let self inductances, mutual inductances, capacities and resistances
bo designated by L or I, M or m, C or c, J? or r with the same sxxffixes
when they apply to the same circuit, the mutual inductance having two
sxffflxcs. Lot I be 3 jt times the munber of complete periods per second,

or b ss Sm The quantities 6L, IM or ^ are of the dimensions of
resistance and thus l^LG or VMO have no dimensions. VLM, ^

or ^ have dimensions of the square of resistances.

Where we have a mutual inductance M, 3 , we have also the two self
inductances of the coils and L*. When these coils arc joined in the
two possible manners, the self inductance of the whole is
Jyj -t- 3il/'jj or 2/j + J>j — .

In case of a twisted wire coil the last is very small. Likewise
LiJjj, — will be very small for a twisted wire coil, as is found by
multiplying the first two equations together.

If there are more coils we can write similar equations. For three
coils wo have

296

Hbnet a. Bowland

+ Zrj 4* Zkj + 2Af5^3 + 2-3f^ 4- 2

1. Zj+ij+Aj — 2Jf^ —

2. Z1+Z3+Z3 — 2Jf^-l-2A^ — 2A^

3. Zi+Z,4Z3+2ify-2Jfi8-2if,8
Coimectnig them in pairs, we have the self inductances

Zj + Zj + 2 Zi -h Zq 4 2 Afjg Zj 4 Zj 4 2ils^8

A4Z3~2Jfi3 A+A-2-a^*i8 z,4Z3-2ii/,3

There are many advantages in twisting the wires of the standard
inductance together, hut it certainly increases the electrostatic action
between the coils. This latter source of error must be constantly in
mind, however, and, for great accuracy, calculated and corrected for.
But by proper choice of method we may sometimes eliminate it.

For the most accurate standards, I do not recommend the use of
twisted wire coils, at least without great caution. But for many pur-
poses it certainly is a great convenience, especially where only an
accuracy of one per cent is desired. In some’ calculations I have made,
I have obtained corrections of from one to one-tenth per cent from
this cause.

For twisted wires the above results reduce to 3Z + 6Jlf, 3Z —
Similar equations can be obtained for a larger number of wires. For
twisted wire coils, n wires joined abreast, the self induction is

which is practically equal to L or M. The resistance

is B/n.

When we have n = wires twisted and wound in a coil and we
connect them p direct and m reverse, the resistance and self induction
will be

nJff-hi^BtAO+BC—fiAB] IPfnCA + B) ^ G^+b^ABO

i:nRf^(wy (kBfT'(ioy »

where B is the resistance of one coil and

A=Z 4(n-l)ilf
B=L - M
0 =wZ4 (4:mp—n)M.

This gives self inductances and resistances equal or less than L and B.
The correction for electrostatic induction remains to be put in. For
the general case, the equation is very complicated for coils abreast,
with mutual inductances.

The number of mutual inductances to be obtained is M for two
wires, 0, Jf, 2Jlf for three wires, 0, AT, 21f, 3ilf for four wires, etc. From

ElBOTiaOAIi MBAStrEEMBKT BY AjMXmXTWQ CUBBENTS 297

these results we see that we axe always able to reduce mutual to self
mductauce. Heasuriug the self iuductauce of a coil counected iu
difiereut ways, we cau always determine the mutual inductances in
terms of the self inductances.

Thus we need not search for methods of directly comparing mutual
inductances with each other, although I have given two of these, but
we can content ouisdves with measuriug self inductances and capaci-
ties. Fortunately most of the methods are specially adapted to the
latter, the ratio of self inductance to capacity beiug capable of great
exactness by many methods.

In tile use of condensers I have met with great difficulty from the
presence of electric absorption. I have found that this can be repre-
sented by a resistance placed in the circuit of the condenser, which
resistance is a function of current period.

I have developed Maxwell’s theory of electric absorption in this
manner. Correcting his equations for a small error, I have developed
the resistance and capacity of a condenser as follows:

Let a condenser be made of strata of thicknesses etc., and
specific induction capacities Ic^ etc., and resistances pi etc. Then
we have

R = ^ — ^ + ^ — etc.

where

= (4ff)‘ I }

etc.

^ = + •»«.}
etc.

Mr. Penniman has experimented iu the Johns Hopkins University
laboratory with condensers by method 26 and found some iuteresting
results. With a mica standard condenser of i microfarad he was not

S98

Henet a. RowLAin)

able to detect any electric absorption, althougb I have no doubt one
of the more accurate methods mU show it.

With a condenser, probably of waxed paper, he found

Number of complete Oapaoity in Apparent resistance

periods per second. miorofamds. In ohms.

14-0 4:-64 139-6

3^-0 4-96 34-1

53-3 4-96 20-5

131-1 4-94 6*2

The first yalue of the capacity seems to be in error, possibly one of
calculation. However, the result seems to show a nearly constant
capacity but a resistance increasing rapidly with decrease of period, as
MaxwelFs formulae show. The constant value of the capacity remains
to be explained.

Mr. Penniman will continue the investigation with other condensers,
liquid and solid, as well as plates in electrolytic liquids.

The results in the other measurements have been fairly satisfactory,
but many of the better methods have only been recently discovered and
are thus untried. But we must acknowledge at once that work of the
nature here described is most liable to error. Every alternating cur-
rent has, not only its fundamental period, but also its harmonics, so
that very accurate absolute values are almost impossible to be obtained
without great care. To eliminate them, I propose to use an arrange-
ment of two parallel circuits, one containing a condenser and the other
a self-inductance, each with very little resistance. The long period
waves will pass through the second side and the short ones through the
condenser side. By shunting off some of the current from the second
side, it will be more free from harmonics than the first one.

However, in a multipolar dynamo, especially one containing iron,
there is danger of long period waves also, which this method might
intensify. A second arrangement, using the condenser side, might
eliminate them. However, many dynamos without iron and without
too many poles and properly wound produce a very good curve without
harmonics, especially if the resistance in the circuit is replaced by a
self inductance having no iron. These remarks apply only to absolute
determinations. Eatios of inductance, self and mutxial, and capacity
are independent of the period, and thus it can always be eliminated.
Measurements of resistances also are independent.

But there are other errors which one who has worked with continuous

Eleotrioal Measitrembn't bt Alternating Currents 299

currents may fall into. Nearly all alternating currents generate elec-
tromagnetic waves which are so strong that currents exist in every
closed circuit with any opening between conductors in the vicinity.

We eliminate this source of error by twisting wires together and other
expedients. But in avoiding one error, we plunge into another. For,
by twisting wires we introduce electrostatic capacity between them,
which may vitiate our results. Thus, in methods 23 or 24 for com-
paring mutual inductances, if there is electrostatic capacity between
the wires, a current will flow through the electrodynamometer in the
testing circuit and destroy the balance.

Various expedients suggest themselves to eliminate this trouble, as,
for instance, the variation of the resistance A in the above, but I shall
reserve them for a future paper. I may say, however, that it is some-
times possible, as in method 12 for instance, to choose a method in
which the error does not exist.

However, with the best of methods, much rests with the experimenter,
as errors from electromagnetic and electrostatic induction are added
to errors from defective insulation when we use alternating currents.

These errors are generally less than one per cent, however, and intel-
ligent and careful work reduces them to less than this.

The following methods generally refer by number to the plate on
which the resistances, etc., are generally marked. One large circle
with a small one inside represent an electrodynamometer. Of course
the circuit of the small coil can be interchanged with the large one.
Generally we make the smaller current go through the hanging coil.

By the methods 1 to 14, we adjust the eleetrodynamometer to zero
by making the phase difference in the two coils 90®. For greatest
sensitiveness, the currents through the two coils must be the greatest
possible, heating being the limit. This current should be first calcu-
lated from the impedance of the circuit, as there is danger of making
it too great.

In the second series of methods, 16-26, the branch circuit in which
the current is to be 0 is indicated by 0.

Besistanoes in the separate circuits are represented by 7?, J2', etc.,
and r, etc. Corresponding self inductances and capacities in the
same circuits are Zr, L', etc., and Z, Z', Z^, etc., or 0, O', Op etc., and
c, c', etc. J = %nn whore n is the number of co-mplete current waves
per second.

The currents must be as heavy as possible, ampere or more, and it
is well to make those that require a current of more than ^hr 8^P®to of

300

Hbnbt a. EowIiAOT)

larger wire freely euspended ia oiL A larger cnrrent can, however, he
passed through an ordinary resistance hox for a second or two without
danger. A few fixed coarse resistances, of large wire in air or ofi. with
ordinary resistsnce boxes for fine adjustment, are generally all that
are required. Special boxes avoiding electrostatic induction are, how-
ever, the best, but are not now generally obtainable.

In some methods, such as 8, 9, 10, etc., we can eliminate undesirable
terms containing the current period by using a key which suddenly
changes the connections before the period has time to change much.

In using twisted wire mutual inductances, methods 1' and 13 are
about or entirely free from error due to electrostatic action between
the wires. In all the methods this error is less when the resistance of
the coils is least and in 33 and 34 when A is least. In method 8 the
error is very small when the coil resistances and 22 are small and t great.
In this method with 1 henry and 1 microfarad the error need not
exceed 1 in 1000. Probably the same remarks apply to 9, 10, 11, also.
By suitable adjustment of resistances in the other method, the error
may be reduced to a •miTn'TrmTin . It can, of course, be calculated and
corrected for.

An electrodynamometer can be made to detect ‘0001 ampere without
TnalriTig the self inductance of the suspended coil more than -0007
henrys or that of the stationary coils more than -0006 henrys, the
latter coil readily sustaining a current of amperes without much
heating.

An error may creep in by methods 1-14 if the current through the
suspension is too great, thus heating it and possibly twisting it. This
should be tested by short circuiting the suspended coil or varying the
current. For the zero method it is eliminated by always adjusting
until there is no motion on reversing the current through one coil.

Inductances containing iron introduce harmonics and vary with cur-
rent strength. Thus they have no fixed value.

Closed circuits or masses of metal near a self inductance, diminish
it, and increase the apparent resistance which effects vary with the
period. Short circuits in coils are thus detected.

Electrolytic cells act as capacities which, as well as the apparent
resistance, vary with the current period. They also introduce har-
monics. The same may be said of an electric arc.

A-n incandescent lamp or hot wire introduces harmonics into the
circuit.

Hysteresis in an iron inductance acts as an apparent resistance in

ElbotbioaIi Measurement by Ambbnating Currents 301

the -wire almost mdependent of the current period, and does not, of
itself, introduce harmonics. The harmonics are due to the variation
of the magnetic permeability witii the amount of magnetization.

Electric absorption in a condenser acts as a resistance varying with
the square of the period, the capacity also varying, as I have shown
above.

In general any circuit containing resistances, inductances and capaci-
ties combined acts as a resistance and inductance or capacity, both of
which vary with the current period, the square of the current period
alone entering. For symmetry the square of the current period can
alone enter in all these cases and those above.

Hence only inductances containing no iron or not near any closed
metallic circuits have a jSbced value. The same may be said of con-
densers, as they must be free from dectric absorption or electrolytic
action to have constants independent of the period. There is no ap-
parent hysteresis in condensers and the constants do not apparently ,
vary with the electrostatic force.

The following numbers indicate both the number of the method and
the figures in the plate, p. 302.

Method i.

Method 2.

-oxyLL'ox- =

ZB,(.r+ R")+^ Jr±A)}

Method S.

In (1) make B' = B!' = B„ = 0 or in (2) make W =:B, = 0, B„ = eo,
E. = rE

In case tixe circnit r contains some self inductance, I, 'we can correct
for it ky the equation

In methods 1 to 14 inclusive the concentric circles are the colls of the electro*
dynamometer. Either one is the fixed coil and the other the hanging coll. Oblong
figures are inductances and when near each other, are mutual Inductances. A pair
of cross lines is a condenser.

ElBOTHIOAL MeASUEBMBNT BT AlTBBNATING CtTEBENTS 303

Method 4-

Method 5.

A _ [ie,(7r + iU + A’.(-K"H-i2')] [A' (i2"+iOH-»-(i2' + i2")]

Method 6.

^ oi^= (R+B') iB"+r)

We can correct for self inductions, L', L" in the circuits B', R" by
using the exact equation

(r+R") + R' ] " L" (B+Bf) + B"(L+ 1') J +

miH'irJflV') {R+R') = (i

or approximately

f =(7i+7i0 (7e"+r)-f -f

+ etc.

Method 7.

B,B,M„M„+b^iL,M,,-MM = 0

For a coil containing three twisted wires, Jlfu = Jfij = Ifg, and the
self inductions of the coils are also equal to each other and nearly equal
to the mutual inductions. Put an extra self induction in Bg and a

capacity Og in Ej. Replace i, by Ir + Lg and Lg by L — ji^^and we
can write

BJi^+b^ (L-M) (Lg+L-M).

As i — M is very small and can be readily known, the formula will
give . When L — JIf = 0 we have

Method 8.

y +/■,) = r 72 WM =>7?+(r72y

or J* M{_M- L) = (r72)' 3S> LM= rR- (rR)'

304

Hbnbt a, EowiiaiD

Placing a capacity in. the ciicnit JB, we have also
or ¥M{_M-L) + :^= rJ2

In case the coil is wound with two or more twisted wires, M — L is
gTma.n and known. For two wires, M — L is negative. For three
wires, two in series against the third, M can be made nearly equal to
SL. Hence M, L and G can be determined absolutely, or 0 in terms
of M or vice versa.

To correct for the self iadnction, I, or r we have the exact equations

L) = rR+in(^l+M)

5‘Jf (Jf-i) = rR+m {L-M)

VM{MJr L)-^ = rR + m{L-¥M—

VM{M—L) + ^ =rR + bn{L-M— ^

If the condenser is put in r, we have

= rR-t^M^L+M)

or k^^rR + VMiL-M)

Method 9.

VL'M-f, = R, \r’ + R,+

or - i^L'M + -^ = [12' + R,+

Making 12" = oo and r + 12' = r we have

- ¥L'M+ y or ¥LM- = R, (r + 12,)

TaMng two otservations we can eliminate ¥L'M and we have
§=RAr-(r)'\

Knowing L'M we can find O'. Throwing ont C (i. e., making it
oo ) we can find l^L'M in absolute measure : then put in O' and find its
value as above.

To correct for self induction iu 12„ we have for case B" = oo , the
exact equation

Elbotrioal Measurement bt Alternating Currents 305

= iZ, (r + i?,) + 6 « \^U ^L,- MIL,-

The correction, therefore, nearly yanishes for two twisted wires in a
coil where L' — M = 0 and 0 is taken out.

Method 10.

-mM+^ovmM-^=

€ C

C^' + jK" + jK^ +

This can be used in the same manner as 9 to which it readily reduces.
But it is more general and always giyes zero deflection when adjusted,
howeyer M is connected. To throw out 0 make it oo .

Method 11.

rB+i' (],-M){L-M)

- ^ rB+S’ (1 + M)(L + M)

For the upper equation the last term may be made small and the
method may be useful for determining L — M when c is known.
Method 8, howeyer, is better for this.

Method 12.

I “r ”

Should the circuits R and r also haye small self inductances, L and Z,
we can use the exact equation

When L' and I are approxiinately knoTO, we can write the following,
using the approxiinate value on the right side of the equation
n _B+Bfr-, , Lr L r . J^Ll . H

T - r l^ + m~ 7"}5!+7if + TB' + J

Taking out L' and putting a condenser, O', in iJ we have

■mOB(B+B')
For a condenser, B can be small or zero.

306

Hbnbt a. Eowland

Method IS.

(A) [bL"- 3^,]’ =

This detennines capacities or self mductions ia absolute value. As
described above, mutual inductiou can also be determined by convert-
ing it into self induction.

(i) [ji„- sy =

TO =

llV'B,-R’R,.-]ZR ..(r+ R ;)+RAr+Rf') ]
Ie(r+B,)

[RfR^.-If'R,-] [R, (r+R")+R,, (r+iZ,)]
" iZ"[f+ii!"+.Bj

Method IJf..

[R,RI'-R,.M-\ [r [R! + R,-\-E'+ i2„] + IR' + iZ J [iZ" + RJ ]

R,Xr+R''+R^

Of coTirBe, in any of these equations, methods 13 or 14, L" is elimi-
nated hy makmg L" = 0 or Ihe condenser, C, is omitted hy making
G = aa.

Method 16.

, or 1^L,L" or

b’0,G' ‘ 0"

MR,, iR,+R,,^(^'+R''2-R^'R.R''R,.

0" L, „ r ,v>_ R,„R"'R,-R'R,. CR.+R,,
^OT^Ot-bL,t ^

When = oo we have

^^ MR„ ^R'^Rp-M'R,R"' ^ _ R^

VL,0"

R"'R,-R'R,,

" ■'iz"iz"' ■

If we adjust hy continuous current, we shall have R'"B, — B'R„ = 0.
For a condenser we can made B" = 0 provided there is no electric
absorption. In this case b^L,0" is indeterminate and we can adjust

to find -^z,. However, two simultaneous adjustments are required.

But I have shown that the presence of electric absorption in a con-
denser causes the same effect as a resistance in its circuit, the resist-
ance, however, varying with the period of the current. Hence R" must

Elbotbioai Mbasxtkbmeni by Altbeitating Cuebbitts 307

include this reBistaneo. However, the value of B" will not affect the
first adjustment much and so the method is easy to work. If it is
sensitive enough it will be useful in measuring the electric absorption
of condensers iu terms of resistance.

It has the advantage of being practically independent of the current

period for ^ as it should be.

For comparison of capacities the same simplification docs not occur.
Indeed tihe method is of very little value in this case, being sur-
passed by 16.

Method 16.

(A) [TP-|-r'+r"]+ = 0

(F/o

The first equation is satisfied by adjusting the 'Wheatstone bridge so
as to make

(B,B"—BJif) =0 Ii/'-Ry=6 B, (i2„ ■+■/') -B,, (7i' +»•') =0
That is

R, -1'

"We can then adjust F with alternating currents. This is a very
good method and easy of application but requires many resistances of
known ratio. Many of these, however, may be eqxial without disad-
vantage. A well known case is given by making r' and r" = 0.

(B) By placing self inductions or condensers in B , and r" instead
of the above we have the following

B'B,,-BXW+2y')

or - 5 L/. or

(F-l-r^-h /0 (R,B''-B.fB')+ W(Ry'-By)

Making B" = 0 we have

or - or y, = '

- ~ (l+ ^)- F

In case we adjust the bridge to BiW — JB'J2,,=5 0 and a condenser

308

Hbnbt a. Bowlaot

is in r" so that we can make r" =0, the value of —h%c" will be inde-
terminate and we can find ^ by the adjustment of W alone.

I C

This is an eicdlent method, apparently, as only one adjustment is
required.

However, see the remarks on method 16. This present method
^ ® ^0^ — is Anderson’s with, however, alternating currents instead

of direct as in his.

The other two values are inoaginary in this case. Indeed the whole
method, B, is only of special value for as two adjustments are needed
for the others.

Method 17.

(A) W= CO. It = CO

i>ML'= R,E’ -

1/ __B'+B,+M'+B,.

M “

By this method the self induction of the mutual induction coil is
eliminated. But it is difficult to apply, as two resistances must be
adjusted and the adjustment will only hold while the current period
remains constant The same remarks apply to B and 0 following.

(B) 11=00.

(B"+B J

( 0 ) W= 00

h’MZ'= (B^"-B'B„)

A_(jy+ii!,) (jy’+izj

M RJRjf

Method 18.

B,B"-B'B,, = 0

= 1 +

, M+B"

L' and M' belong to the same coil. By adjusting the Wheatstone
bridge first, W can then be afterwards adjusted.

ElBOIRIOAIj llBAStTKEMBlTT BT AlffBBNATING OtTBEBSTTS 309

To find tie ratio for any other coil independent of the induction coil,
■we can first find as above. Then add L to the same circuit and we

can find — Whence we can get L. This seems a convenient

method if it is sensitive enongh, as the val'ue of ^ should he accurately
known for the inductance standard.

M^iod 19.

.Vi? +5, R’B„-R"B.(l

^ ^

This is useful in obtaining the constants of an induction standard.
For t'wisted wires L'l — Aould be nearly 0, depending, as it does,

on the magnetic leakage between the coils. ^ is often known suflS-

ciently nearly for substitution in the right hand member. It can,
however, be fo'und by reversing the inductance standard.

Method SO.

R'R„ - Rf'R, = 0

M_ R„ . M_ W R* . L W

-L-K+R~’ V = R^+2f>

11 any value.

L>M%

In case of a standard inductance, M and L are known, especiaUy
when the wires are t-wisted.

The method can then bo used for determiumg any other inductance,
L', and is very convenient for the purpose.

R,! and + R,, are first calculated from the inductance standard.
The Wheatstone bridge is then adjusted and W varied until a balance
is obtained. This balance is independent of the current period, as also
in the next two methods.

Mtihod M.

RIR„-R!'R^z=9

i + L'_(^RI + Ry, TJ R'^Rn^xr

M~ -r;- -M- rlt, ’ 1 = ■ • r ■

This is ITiven’s method adapted to alternating currents. See re-
marks to method 20.

310

Henbt a. Eowland

Methods 20 and 21 are specially useful when one wishes to set up an
apparatus for measuring self induction, as the resistances B', B",
Bfl JS,, can be adjusted once for all in case of a given induction standard
and only Tf or r need be varied afterwards.

Method 22.

U'_B!-\-R, M_
M ITT’ a~

This is Carey Foster’s method adapted to alternating currents and
changed by making B" jSnite instead of zero.

The ratio of E' + jB/ to is computed from the known value of
the induction standard. B" is then adjusted and O' obtained. In
general the adjustment can be obtained by changing B^ and B". The
adjustment is independent of the curaent period.

Method 28.

IhnL' = rR,+B\r+E+B;\
m ' ^ /

If we make i2 = 0 we have

VmL' = rR^
m T

This method requires two simultaneous adjustments, JIf must also
be greater than m. As Jf and H belong to the same coil, wo can con-
sider this method as one for determining m in terms of the M and 7/ of
some standard coil.

The resistance, A, can be varied to test for, or even correct, the error
due to electrostatic action between the wires of the induction standard.

Method IBJ/..

^ This is a good method for comparing standards. Wo first dotennino
for each coil by one of the previous methods. Then we can calcu-

Iftic ^ 8nd adjust the other resistances to balance.

It is independent of the period of the current and suitable for stand-

Elbotbioaii Measubbment by Alxebitaying Cubbenxs 311

ards of equal as well as of different values, as the mutual inductances
can have any ratio to each other.

For twisted wire coils r,e=r' very nearly. See method 33 for the
use of the resistance, A.

Method 26.

In Pig. 6 remove the shunt R' and self induction L.

This method then depends upon the measurement of the angular
deflection when a self induction or a capacity is put in the circuit of
the small coil of the electrodynamometer and comparing this with the
deflection, when the circuit only contains resistance.

The resistance of the circuit, r, is supposed to be so great compared
with R that the current in the main circuit remains practically un-
altered during the change.

There is also an error due to the mutual induction of the electro-
dynamometer coils which vanishes when r is great.

These formulae assume that the deflection is proportional to 6. This
assumption can be obviated by adjusting 0 = 6' when we have

These can be further simplified by making JB " = i?/'.

The method thus becomes very easy to apply and capable of con-
siderable accuracy. As the absolute determination depends on the
current period, however, no great accuracy can be expected for absolute
values except where this period is known and constant, a condition
almost impossible to be obtained. The comparison of condensers or of
inductances is, however, independent of the period and can be carried
out, however variable the period, by means of a key to make the change
instantaneously.

Method 28.

Similar results can be obtained by putting the condenser or induc-
tance in R" instead of r, but the current through the electrodynamo-
meter suspension is usually too groat in this case unless r is enormous.
We have in this case for equal deflections.

where r, and B/' are the resistances without condenser or self induction.

312

Hbnbt a. Eowland

TMs is a very good method in many respects.

Por using 26 and 26, a key to make instantaneous change of connec-
tions is almost necessary.

To measure resistance by alternating currents, a Wheatstone bridge
is often used with a telephone.

I propose to increase the sensitiveness of the method by using my
method of passing a strong current through the jSjced coils of an
electrodynamometer while the weaker testing current goes through the
suspended system.

Using non-inductive resistances, methods 10, 13 A, B, (7, and 14 all
reduce to proper ones. 10 or 14 is specially good and I have no doubt
will be of great value for liquid resistances. The liquid resistances
must, however, be properly designed to avoid polarization errors. The
increase of accuracy over using the electro d 3 mamometer in the usual
maimer is of the order of magnitude of 1000 times.

Since writing the above I have tried some of the methods, especially
6 and 12, with much satisfaction. By the method 12, results to 1 in
1000 can be obtained. Eeplacing U by an equal coil, the ratio of the
two, all other errors being eliminated, can be obtained to 1 in 10,000,
or even more accurately.

The main error to be guarded against in method 12, or any other
where large inductances or resistances are included, arises from twist-
ing the wires leadiag to these. The electrostatic action of the leads,
or the twisted wire coils of an ordinary resistance box, may cause errors
of several per cent. Using short small wire leads far apart, the error
becomes very small.

Method 6 is also very accurate, but the electric absorption of the
condensers makes much accuracy impossible unless a series of experi-
ments is made to determine the apparent resistance due to this cause.

In method 12 I have not yet detected any error due to twisting the
wires of coils 1. However, the electrostatic action of twisted wire coils
is immense and the warning against their use which I have given above
has been well substantiated by experiment. Only in case of low resist-
ances and low inductances or m cases like that just mentioned is it to
be tolerated for a moment. Connecting two twisted wires in a coil in
series with a resistance between them, I have almost neutralized the
self induction, which was one henry for each coil or four henrys for
them in series !

Altogether the results of experiment justify me in claiming that

ElBOTBIOAL MbASXJEEMENT BT AlTBBN’ATIN’G- Cukrbnts 313

t]i6se methods will take a promiiieixt place in electrical measurement^
especially where fluid resistances, inductances and capacities are to be
measured. They also seem to me to settle the question as to standard
inductances or capacities, as inductances have a real constant which can
now be compared to 1 in 10,000, at least.

The new method of measuring liquid resistances with alternating
currents allows a tube of quite pure water a meter long and 6 mm.
diameter having a resistance of 10,000,000 ohms to be determined to 1
in 1000 or even 1 in 10,000. The current passing through the water
is very small, being at least 600 times less than that required when the
bridge is used in the ordinary way. Hence polarization scarcely enters
at all.

It is to be noted that all the methods 16 to 24 can be modified by
passing the main current through one coil of the electrodynamometer
and the branch current through the other. The deflection will then be
zero for a more complicated relation than the ones given. If, however,
one adjustment is known and made, the method gives the other equa-
tion.

Thus method 18 requires 22,5"— = Hence, when this is
satisfied we must have the other condition alone to be satisfied. Also in
method 22, when we know the ratio of the self and mutual inductances
in the coil, the resistances can be adjusted to satisfy one equation while
the experiment will give the other and hence the capacity in terms of
the inductances.

Again, pass a current whose phase can be varied through one coil of
the electrodynamometer, and the circuit to be tested through the other.
Yary the adjustments of resistances until the deflection is zero, how-
ever the phase of current through the first coil may be varied.

The best methods to apply the first modification to are 16 A, 16 A
and 2?, 18, 20, 21, 22 and 24. In these, either a Wheatstone bridge can
be adjusted or the ratio of the self and mutual inductances in a given
coil can be assumed as known and the resistances adjusted thereby.

The value of this addition is in the increased accuracy and sensitive-
ness of the method, an increase of more than one hundred fold being
assured.

As a standard I recommend two or three coils laid together with their
inductances determined and not a condenser, even an air condenser.

BLECTEIOAL MEAStTElEMENTS

Bt Hbnbt a. Rowland and Thomas Dobbin Fbnniman
[American Journal of Scisnce [4], FJ/J, 86-67, 1899]

In a previous article ^ mention was made of some work then "being
carried on at the Johns Hopkins University to test the methods for
the measurement and comparison of self -inductance, mutual inductance,
and capacity there described.

In ihe present paper, there will be given an account of the experi-
ments performed with some of the methods described in the previous
article, together with a method for the direct measurement of the
effect of electric absorption in terms of resistance.

The methods that were tried were 25, 26, 9, 3, 12 and 6.

Appabattts

Besoriftim of the EUdrod/ynamometer, Dynamos, Coils, Condensers,
Resistances and Connections used m the Experiments

Electrodynamometer. — The electrodynamometer was one constructed
at the University, having a sensitiveness, with the coils in series, of 1
scale division deflected for -0007 ampere.

The hanging coil was made up of 240 turns of No. 34 copper wire B
and 8 gauge. The coil was suspended by a bronze wire connected with
one terminal of the coil. The other terminal of the coil was a loop of
wire hanging from the bottom of the coil and attached to the side of
the case; both the suspension and the loop were brought out to binding
posts. The resistance of the coil with suspension was 21-7 ohms.

The fixed coils were made up of 300 turns each of No. 30 B and 8
gauge copper wire. The coils were wound on cup-shaped metal forms
and soaked in a preparation of wax. The form was then removed and
the coils placed a radius apart as in the arrangement of Helmholtz.

Dynamos. — There were two dynamos used, a Westinghouse alter-
nator, and a small alternating dynamo constructed at the University.

Jonrixal, iv, p. 439, December, 1897; Fbilosophical Magazine, January, 1898.

EI(II03?IU:oaL MSABUBElfEINTS

315

The Westinghouse dynamo was one having 10 poles so that each revo-
lution of the armature produced 6 complete periods. The period of
this dynamo was determined by taking the time of 1000 revolutions of
the armature. This was accomplished by having the armature make
an electric connection with a hell every 200 revolutions and tnlfing the
time of 5 of these. The taking of the speed during every experiment
gave more regular results, as the speed was constantly changing, the
dynamo being run by the engine in the University power-house when it
was subject to great change of load. This dynamo had a period of
about 132 complete periods per second.

For the production of a current of less period than that of the West-
inghouse, the small alternator constructed at the University was used.
This dynamo was run by a small continuous Sprague motor. The arma-
ture of the small alternator consisted of 8 coils, which coils were fas-
tened flat on a German silver plate, the plate revolving between 8 field
pieces producing 4 poles. The object of having the coils of the arma-
ture on a metal plate was to secure a nearly constant speed. The metal
plate produced a load that varied as the velocity and due to induced
currents in the plate. The varying load, depending on the velocity of
the moving plate, produced a nearly constant speed, which rendered
unnecessary the constant taking of the speed. When this dynamo was
used, the speed was only determined two or three times during a series
of readings or experiments. The average of these determinations was
taken as the speed during the whole series of experiments under con-
sideration.

Cotfe.— The coils whose inductances were determined were all made
in the same way, being wound on a metal form and soaked in a prepa-
ration of wax. When the wax was hard the metal form was removed.
This enabled the coils to bo placed close together, as thoir sides were
flat and smooth.^ The coils all had the same internal and external
diameter, but their width varied, that being determined by the number
of turns that were desired.

Coils. Pi. External diameter 36*46 cm., internal diameter 23*8
cm., was made up of about 1200 turns of No. 16 B and 8 gauge single
covered cotton copper wire, roughly wound ; the turns were not smooth:
•self-inductance as finally determined *666 henry.

Pj. Same dimensions. Turns were put on evenly. The number
of turns was 1300 of No. 16 B and 8 single covered cotton copper wire.
Self-inductance *724 henry.

A. Same internal and external diameters as P, but the width was

316

Hbioit a. Botoaot

4-3 cm. ’NumheT of turns 3700 No. 20 B and 8 gauge single covered
cotton copper ■wire. Self -inductance as determined 6 ‘30 henrys.

J5i Bg. TMs coil was made by winding two wires in parallel and all
four of the terminals brought out to binding posts. Thus the coils
could be used as two single coils, when the coils will be denoted by the
symbols 5^ and as the case may be, or as a single coil, the coils B^
and B^ being joined up in series or in parallel. The dimensions of the
coils J5i B^ were the same as A. Each of the coils B^ and Ba were
made up of 1600 turns of No. 22 B and 8 single covered cotton copper
wire. The self-inductance of these coils taken separately when com-
pared with P, which was determined absolutely, was nearly 1 henry.
On this account B was taken as being 1 henry, and the other coils were
compared with it as a standard.

G. Same dimensions as P^. Number of turns 1747 of No. 22 B and
8 single covered cotton copper wire. Self-inductance as determined
1-30 henrys.

Condensers . — 2 and 3. Two paraiBBlned paper condensers that had a
capacity of 2 and 3 microfarads respectively.

Jd Troy. A ^d microfarad standard mica condenser built by the
Troy Electric Co.

■Jd Elliott. A -Jd microfarad standard mica condenser built by Elliott
Bros.

Besistdnces , — The resistances used in the experiments were of two
kinds, those wound ■with double "wire so as to have no self-inductance,
as the ordinary resistance box, and those wound on frames or cards
which had some small self-inductance, but almost no electrostatic
capacity. The resistances which had self-inductance are called open
resistances to distinguish them from resistance boxes, and were of
different kinds and dimensions.

8ovrces of Error and Experimental Difficulties

In all work ■with alternating currents there are two great sources of
error that have to be guarded against. These are the errors that may
arise from the inductance of one part of the apparatus on another, as,
for example, the direct induction of a coil in the circuit on the coils
of the electrodynamometer, and the effect of the electrostatic capacity
of the leads and connections. In connecting the coils great care had
to be taken to avoid the effect of electrostatic action of the leads and
connections. For if there was a current of very considerable magni-

Eleoteioal Mbastjeembnts

317

tude, the difEerence of potential between the terminals of the coil
might be great. If the connections nnder these circumstances were
made with double wire, as is customary, a great error was introduced
due to the electrostatic capacity of the leads. The error was sometimes
as much as 7 per cent (see method 24). This error could be shown to
be due to the electrostatic action of the leads by shifting a resistance in
circuit with the coil in question from one end of the double wire to
the other . The effect of this was to still further increase the difference
of potential between the leads, and this increased the error. Experi-
ments of this character showed the necessity of using open leads and
open resistances having little or no capacity in all cases in which the
coils experimented on and the resistance boxes used in their determina-
tion have a current of any considerable magnitude passing through
them. In several of the following methods constancy of current was
necessary. This was accomplished by various means that will be de-
scribed in their actual application.

Methods

The methods that were tried were 26, 26, 9, 3, 12 and 6 described in
this Journal, December, 1897.*

Method 26 . — ^Method of equal deflections. Absolute method for the
determination of self -inductance or capacity in terms of electromagnetic
units.

In this method the hanging coil is shunted oft the fixed coils circuit,
and this with a non-inductive resistance in circuit with the hanging
coils is made the same as that of a certain inductive resistance in cir-
cuit with the hanging coil. The connections are made as in the Figs*
1, 2, where are currents* iZ, JB', r, resist-

ances. They represent the entire resistance of their respective branches.
L represents self-inductance of the coil by which it is placed. The
outer circle in Pig. 1 represents the fixed coils and the small circle the
hanging coil of the electrodynamometer. In Pig. 2 the terminals of
the fixed and hanging coils are represented by F and E, D is a revers-
ing commutator. £* is a key to send the current first through the
inductive and then through the non-inductive resistance. 65=2 to,
n=: complete alternations per sec. This is the general notation adopted
throughout the article.

“Phil, Mag^., January, 1808 .

318

Henet a. Eowland

The quantity to be found is O^Oi eoBf»i, 'W'bicb is proportional to
the deflection of the hanging coil in the two positions of K.

In one position

Therefore

O^Oi cos = O',

(i24-r)*+3^7?

«i>

In the other position of K

- ai®*") r

C,Cl = Ol

ITTr

« zy

Therefore

Eleoibical Measubemehts

319

0, as <l> is an angle whose tangent is ^ and 0 = 0 nearly. In the
case of equal deflection D = D' and therefore
V^Dr={IS-R) (J?+r)

If capacity had been used in the place of self-inductance the formula
would be

If self-inductance and capacity were used in series

The application of this formula to the measurement of self-induc-
tance gave results that agreed to within the accuracy with which the
period of the alternations could be determined. That is, the results
agreed to within about 1 per cent. In the determination of L the
resistance in circuit R was varied from the least possible resistance as
determined by the coils up to 1000 ohms and more, . and the self-
inductance was determined under these various conditions. These
results agreed among themselves, and were apparently independent of
the resistance in circuit with it. In the application of this method to
the determination of capacity, however, great trouble was encountered,
as the capacity apparently varied both with the resistance in circuit
with it and with the period. This variation was regular for each period,
the value derived depending on the resistance in circuit. This irregu-
larity of derived value of the capacity led to the investigation and
development of Marwcll’s formula on the effect of absorption, a neces-
sary characteristic of heterogeneous substances.

When the formxila was deduced, as may bo seen in the article already
referred to, the absorption comes in ns an added resistance, the resist^
ance being constant for a given period. By an inspection of the results
this was found to bo the case. The finding of the resistance due to
absorption in .this method is one of approximation, but the values
deduced compare very favorably with those determined by direct meas-
urement, as will bo seen later when various results are collected. In
the actual experiments the condensers xised wore two jiaraffined paper
condensers of about % and 3 microfarads. The cxirrents used had
different periods, as seen in the table following, where n = 188, 58-8,
31 -9 and 14.

The process was to place in the condenser circuit a resistance B, and

Hbnbt a. Eowlaot

dso

then to ip. 0 Te the key K hack and forth nntil R' was found that gave
tile same deflection. ID, Fig. 2, was now reversed and the process
repeated. This was repeated witii different values of B and n and the
apparent capacity. This gave great variation of apparent capacity with
different values of B, which should not he the ease, and, therefore,
gave a means of fluding the resistance due to absorption or absorption
resistance, as we will designate, by approximation. As the effect of
absorption is a resistance it is possible to And what resistance, if added
to B, will make all the values of the capacity as determined for the
different values of B the same. Therefore it should be the same for
any two values of B. Calling the two values of in the two eases
and B^ respectively and the two corresponding values of B', B^, and
R^, and let A be the added resistance due to absorption, the capacity
should be the same in the two cases, or

(i?,+A)] [A:,+ A+r] = lB^- (i?.+A)] [-i2.+^+r]

From this A is found for the period used. By doing this for a
number of different values of B, the true value of A is approximated.
A was thus found for the condensers 2 and 3 microfarads with different
values of n. The calculations were again performed adding to the
different values of S a constant resistance A. The capacity that was
found when A is added to i! is called the corrected capacity. In the
table below are collected the corrected values of the capacities together
with n and the resistance A.

Capacity

4*94

4-96

4-64

mlorofaradB.

181-1

68-8

81-98

14-

complete alternations.

6-19

20-6

84-09

189-62

a1}Borption reslBtanoe In olims.

The last value of the capacity seems to be an error, possibly one of
calculation. However, the results seem to show a nearly constant
ca^)acity, but a resistance iucreasiug rapidly with decrease of period, as
Maxwell’s formula shows. The constant value of the capacity remains
to be explained.

But in the above, determinations of absorption resistance are by
approximation. Professor Rowland has, therefore, devised a method
by which it can be measured directly. This method, with the results
that have been derived by it, will now be given.

ElBOTBIOAL MBAStrilBMBN'TS

321

Method for the Direct Medtsv/rement of Absorption Resistance
In a Wheatstone bridge (Fig, 3) let the resistance of the difiEerent
arms he denoted hy B,, E', R,,, R" and r. Let B.have in circuit a
self-inductance and let r have in circuit with it a sdf-inductance,

Let be the current through R, and (7e<C»t + ^) "be ^he current
through r when a periodic electromotive force is applied to a and d in
the figure.

Let OJ be the current through JBy, and O' be the current through r
when there is a constant difference of, potential between a and d. The
ratio of the current in this case is

c' _ R”R,^B'R„

When a periodic electromotiye force is applied to a and i, the ratio
of the currents in this case is

c M _ R"R,-RR„+ihB"L,

7P. ~ lif (R!' + R,) + r (la + J2 ") + ibl (JiT + IH')

Separating the real and imaginary parts

c _ {R!'R-R'R!')[.R'{Rf'^R,

^ cos^>

If noT the filed coils of the electrodynamometer are placed in the
R, arm of the bridge, and the hanging coil is placed in cross connection

of the bridge, as in Kg. i, the different resistances may be adjusted
21

Hbnbt a. Eowlajtd

until there is no deflection, in wMcli case <#>=90® or cos^= 0, therefore

- ISB,;) IB! {B" + iJ J + r (i2' + i2")] + ^IL,B!' (Bf + Br') = 0,

~ B! (JJ" + ij + + '^') ■

If in connection -with i' a capacity C is added, the formula becomes,

substituting for L, — gjj. •

B’B, = Hit., - [mz, - 1 ) ^ ■

In most cases since Z and are generally the self-inductances of the
instrujnents the term hxlL, can be neglected in comparison 'with
and the equation becomes

BI'B, = B!B,,

I B!'(E+B!')

T B>(W+B,) + r(B!+B!Y

In this equation B^ includes both the ohmic and the absorption resist-
ance. The value of Bj is determined in terms of known quantities,
that is the resistance and I and C. It was not necessary that Z and 0
should be exactly known as the last term in the equation above plays
the part of a correction term, and is in all cases below small and in
some cases negligible. The capacities that were used in the experi-
ments were the 3 and 3 microfarads, the i microfarad EUiott condenser,
and the i microfarad Troy condenser.

Experimenis. — The process of ejqjerimenting was to apply a periodic
electromotive force to a and d, and to adjust the different resistances
un'til 'there was no deflection of 'the coil in the same way as in the
ordinary measurement of resistance on a Wheatstone bridge. The
different resistances B', B", B„ and f being known, the apparent value
of the resistance B, was found, and kno-wing the ohmic resistance of
the Bj circuit, the absorption resistance appears as the difference.

ElboibioaIi Mbasxtbbubkxs

323

Some interest lies not alone in that the method is applicable, but that
it confirmed the supposition that absorption resistance acts as an ordi-
nary ohmic resistance in series in the circuit. This was confirmed by
the fact that when condensers were in series and in parallel, their
absorption resistances acted under these conditions like ohmic resist-
ances, being increased in the one case and decreased in the other, and
in the right ratio. This agreement was not exact, as the absorption
resistance was extremely sensitive both to change of period and change
of temperature. The great sensitiveness to change of temperature was
shown either by letting the current go through the condensers for a
little time, or placing the condensers before a hot air flue; in either
case after cooling, the absorption resistance returned to its original
value. The cooling was very slow, as there was very little radiation
from the condensers inclosed in wooden boxes.

The results are now given for the condensers 2 and 3 microfarads.
In the calculation of the results the last term of the equation, that is

4 . small when
condensers 2 and 3 microfarads were used.

OOHSaHBBBB 2 AND 8 HiOBOVABADS XN P ahat.t.bt-
nsl8i, I=*0007 UBt term negligible.

IR//

Beals, of
B' olroult
In ohms.

Beslstanoe
due to
absorption.

422-6

488-6

6467-8

847-9

89-29

88-77

6-80

1488-6

488-2

128-4

40-50

6-78

984*1

82-1

40-72

88-81

6-91

2671*6

22-5

41-116

7-80

428-0

867-8

41-287

7-42

5474-8

((

464-5

41-42

7-61

6784*

((

874-9

41-67

7-86

1 ohm in W*
7486*

«oal6 diyislon.

tt ft

688-6

41-64

7-88

9466*

81-15

41-85

8-04

Condensers 2 and 3 placed before the register and heated

for 1 hour:

7489-7

488-27

718-8

46-584

84-88

12-20

After standing IJ hours in air at temperature of 12 ® -8 0. condenser
has been open so that resistances have been cooled:

1340-6 487-8 <• 109 - 43-86 84 - 8-86

After standing some little time:

7482-5 487-8 •• 651-6 43-47 84 - 8-49

The above table shows conclusively the heating of the condenser by
the current, and the dependence of the absorption upon the temper-
ature.

324

HllTEY A. Bowland

OolTDlDIjlBBBS 2 AND 8 IK PaBALLBL. N= 57 * 6 .

By,

% A

ohms. A.

848-5

488-6

896-8

11020*7

55*61

88*77 21*84

7488-

((

849*2

66*41

21*64

844*1

4026*

65*07

(1 21*80

8485-

((

896*1

65*58

u 21*81

N=66

8486-

*6 per second.
200-24

976-7

4026*

56*00

Average, 21*68

22*28

Comparing these values with those found in the use of method 26
the agreement is at once apparent.

N= 181^^ 57J 66^5 jB8;_

Method 26

Dlrect niea8iire> 6*80 cold 21*68 22*28

ment. 7*00 warm.

It should be remembered, in comparing the results, that the values
obtained by method 26 would naturally be smaller than those found by
direct measurement, as in method 26 the current going through the
condensers was extremely small; there was therefore practically no
heating.

The experiments that confirm the mathematical theory that the
absorption resistance could be treated as ordinary ohmic resistance were
performed with the two condensers, -J Troy and ^ Elliott microfarad
condensers. These are next given.

In these results it was necessary to take into account, in the calcnlar
tion of the apparent value of the last term of the equation, that is

^ Troy and i Elliott ia series, 1 o^clock.

4764*

Apparent
value
of B/
48*141

B" By, B'

4761-8 499*9 404*8

i Troy, 2 o’clock.

4780 • 497 76 853-4

i EUiott, S.46 o’clock.

4749-8 497-67 890-8

i Troy and i Elliott in. parallel, 4 o’clock.

4749-8 497-6 850-28 <* 86-94

i Troy and i Elliott in series.

4748-5 497-66 418-16 “ 44-613

87-388

41-360

Ohmlo roslst-
anoe
of B,
84*148

Absorption

reslBtanoQ

8*998

84*144

8*144

7*116

84*16

2*79

84*12

10*492

El/EOTitlOAL MbaSUEHMENIS

325

Calculating what the absorption resistance should be for J Troy and
J Elliott in series, from the absorption resistances of the two con-
densers when determined separately, it is equal to 10-26 ohms, which is
greater than the first and less than the last value above, showing that
the condensers were heating during the experiments. Calculating the
absorption resistance of i Troy and Elliott in parallel in the same
way, it is equal to 2*209 ohms, which is less than the value afterwards
obtained by experiment for the same reason.

The method was shown not to be based on any false supposition, by
substituting in place of the condenser a coil of known self-inductance.
When this was done the value of jB^ as calculated from the other resist-
ances and the self-inductances should be the same as the actual ohmic
resistance of the circuit.

This was tried with two coils and A and the agreement was re-
markably close, as seen in the next table.

Coil P used in place of condenser in the circuit:

_ Deduced va uo Actual value

B// B' r ofK/ ofR,

474-9 487-8 758-2 6457 - 77-86 77*8

Coil A in place of condenser in the Bj circuit:

474-9 487-8 218*3 224-12 228-9

In these experiments great care was taken that the measurements
of the resistances were performed immediately after the adjustment.
In this way the actual resistances at the time of the experiment were
obtained, and so the effect of the heating by the current was some-
what eliminated.

Methods 26, 9 and 3 give good results, but the methods that gave
the most satisfaction were methods 12 and 6, method 12 being for the
comparison of two self-inductances and method 6 for the comparison
of a self-inductance with a capacity. These give some remarkable
results, the theory and deductions of the methods being as follows :

Method 12, — Zero Method for the Oomparison of two 8 elf -Inductances

Let the connections be made as in the figure where the hanging coil
and the fixed coils are in two distinct circuits.

Let etc. be the currents. A' and A" reversing commutators,
22'', B and r the resistance of the different circuits, JS" and L the self-
inductances, M the mutual inductance of the coils and by which
it is placed. When a periodic electromotive force is applied to
1, B the quantity to be found is 0^ 0^ cos (<^, •— ^0 where
is the difference of phase.

8%6

HhNBT a. BOWIiAND

The current in the R" circuit is then

C?^ei(W + « —

W+iSIP

( 1 )

The current in the B circuit is

(7,e«(6t+W :®±21±i^ =(7.e«>*.

Substituting the Tslue of in equation (1) and simplifying, it
becomes

(7^e<(W+*) =5

<7,e*CW + *i>

— VLM+ibM(B+r)
B!'r-ibL"r —

Therefore the deflection is proportional to

AN n,-i'LMB"r+VI/'Mr(R+r).
0,0, cos = Oi jyv+<^ ^ ’

and the condition for zero deflection is

- VLMBI'r + VL"Mr{R+r) = 0,
L _R±r
" JF~~W’

The condition therefore of zero deflection is independent of M. But
M is one of the factors of the electromotive force in the B" circuit, and
on it therefore depends the sensitiveness, as it determines the current
through the B" circuit. In the flrst figures of this method the fixed
colls are m the B" circuit, and the hanging coil in the B circuit, but
this is not necessary, as the fixed and hanging coils can be reversed.
The choice of frhich of the above arrangements should be used depends

Blbotbioal Meastjeiiments

327

on the impedances of the two circuits, as other things being equal the
smaller current should go through the hanging coil.

Experiments . — The coils used in the experiments were coils P^, Pa,
0, Py Pj, and A, which coils are described on page 316. Prom the
dimensions of Pj and its self-indimtance as found by method 25, P^ was
designed to have a self-inductance of one henry. This will be shown
to be nearly the case. For ease of comparison has been taken in
the calculations of the results as being equal to one henry, and the
other coils were compared with this coil as a standard.

In these experiments the connections were made as in the figure 7,
the coil Pi that was taken as the standard being placed in circuit with
the fixed coils of the electrodynamometer as L" and the resistance of
this circuit was unaltered during the experiments in any particular
series. The coils whose self-inductances were to be determined were
placed in the hanging coil circuit and the resistance B was changed
until there was no deflection. The resistance of the two circuits, B"
and P -|- r were then measured by a 'Wheatstone bridge.

The resistance r was in all cases small in order that Oo®®* should be
large, and therefore by induction 01 **®*+*) the current through the
fixed coils was made large and the instrument sensitive. The method

328

Henry A. Eowland

being very accurate, as will be seen later, great care bad to be used to
eliminate all Bonrces of error, as for example, electrostatic action. In
the first trial of the method small differences were noticed in the ratio
of two self-inductances, depending both on the resistances used, and
also on the connections of the coils, whether the leads were double,
single, long or short. The same variation was noticed when several
coils were joined in series and compared with another coil, and when
these coils were compared separately and their sum taken.

This irregularity led to an investigation of the effects of various
resistances and connections in one of the circuits, the other circuit
being u na ltered. A little farther on, the variation in the deduced value
of the self -inductance of one of the coils, when different resistances and
leads were used, will be given, which variation was caused by the
electrostatic action of the connections, etc. (Page 316.)

The necessity of eliminating electrostatic action made obligatory the
use of open resistances which had small self-inductances. These re-
sistances were of three kinds — ^resistances in the form of spirals, resist-
ances wound on thin strips of micanite or paper, and those wound on
open frames; see page 316.

The self-inductance of the first and second classes of resistances was
very small, as in one case there were only a few turns, and in the other
the cross-section was very small.

The third class were those wound on frames whose self-inductances
were calcxilated. There were several resistances of 2000 ohms each,
whose self -inductances were *0000436 henry, which would hardly affect
the phase of the current or the impedance of the circuit.

These coils were subdivided into resistances of various amounts.
Another frame resistance used was of 7463 ohms divided into parts of
about 250 ohms each. The self-inducxance of the entire 7463 ohms
was *000106 henry.

As the open resistances were not divided ‘into small amounts it was
necessary to use resistance boxes for adjustment; as few ohms as possi-
ble were used in each cas^.

Prom the fact that the coils of the electrodynamometer had self-
inductance a correction was introduced in order that the ratio of the
resistances should give the ratio of the self-inductances of the coils
direct.

The value of this correction in ohms was calculated as follows:

ElBOIBIOAL MBAStTBBUBNIS

329

Calculation of Correction Due to Fixed and Hanging Coils

Self-inductance of fixed coils = / = ‘0164 henry
“ “ “ hanging coil = h = *0007 “

Correction due to fixed coils. From an inspection of the tables it
is seen that

L _E+r L _B+r

W’ i.0164 902’

■where L is the self -inductance of some coil and E -j- r is the corre-
sponding resistance. is taken as equal to 1 henry

L _ 1-0164

•* 902"

But the comparison of L with JBi = 1 is wanted, therefore both numer-
ator and denominator of Me divided by 1-0164 or

L _l=By
• • “ 887-45 ’

. L _ B+r

” ~E ~ B37-46 ■

That is, the self-inductance of -0164 henry of the fixed coils produced a
correction of 887-45 — 902 = — 14-65 ohms, which must be applied to
the B" circuit if the self-inductance of that circuit is to be considered
as 1 henry.

Correction due to hanging coil. The self-inductance = -0164 henry
of the fixed coils gives a correction of — 14-65 ohms, therefore the self-
inductance -0007 henry of the hanging coil gives a correction of • — 62
ohms to the E-f-r circuit. Applying these corrections, the results
obtained for the several coils under various conditions arc given below.
The results are given in the following order.

Fvrd. The values are calculated using double leads in the circuits
but open resistances as far as possible.

Second. The variation of the apparent value of the self-inductancc
of one of the coils -with different positions of the coU, resistances, and
different kinds of leads.

Thkd. Short leads separated about 6 inches and crossed, used with
all the coils except

Fourth. Open leads and open resistances in the determinations. In
the table B" was open resistance plus the resistance of coil B^ and
fixed coils of instrument. E -|- r was made up of the small coU and
open resistance plus the amount in the Queen ordinary resistance box.

330

HeNEY a. EaWLAJSTD

After all the inductive effect of the leads was removed and the ordi-
nary resistance hox used as little as possible, there was a different value
obtained for the ratio of the self-inductances dependent on the position
of the reversing commutator A'. With all the coils used the greater
value occurred with the same position of A!. This was due to the
electrostatic action between the coils and B^^ for if the terminals of
the coil jBa and the commutator A* were reversed at the same time,
there was no change in the value of the ratio of the inductances. This
showed that it was dependent on the coil itself and not on the leads
and it could therefore not be eliminated.

It is to be noticed that the values obtained for the lower number
of alternations are always greater than those found with the higher
number of alternations. This was caused by the electrostatic action of
the turns of the coil on each other. In the case of the coil this effect
would be caused by supposing a capacity of -0007 microfarads shunted
across the terminals.

The results are now given comparing the different coils with B^ as
a standard and equal to 1 henry.

Double Leads or Bell Wire and Open Kesistanoe

r = 106 oluns, n = 45 complete periods per second.

Oolls.

R".

Oorreo.

COT>-

Aver-

Com.

Queen.

R+r.

reo.

age.

A'.

Ratio.

Pl+Pa

+ 0

901-0

-14-55

887-05

292

2800-2

-•62

2804-9

2-5988

((

810

2811-0

((

1158-8

1169-0

1-8099

1161-2

C + P,

108

1669-

1661-3

1-8727

((

109

1664-8

C + Pj

1800-2

1802-6

2-0288

1806-5

901-7

887-15

149

4776-5

4786-6

5-8956

196

4818-0

Ourrent incieased about 2^ times.

((

141

4787-0

4781-8

' 1

5-8898

((

184

4807-

A+C

901-6

887-05

211

5986-

5958-8

6-7170

264

5982-

A + C + Pa

((

6575-5

6602-5

7-4480

((

104

6631-0

902-

887-45

158

4778-9

4796-26

5-4086

((

192

4818-

Pa + Pa

((

188

1146-5

1146-7

1-9923

((

186

1148-5

((

648-15

642-67

•7243

((

648-6

((

603-5

603-16

•5058

((

608-1

Elbotrioal Mbasttrekbkxs

331

DouBLn Lbads. n= about ISS complete alternations per sec.

Correo.

Cor-

Aver-

Com.

OollB.

Queen. K+r.

reo,

age.

A',

Batlo.

901*9

—14-55

887-35

90+s 600-4

+ -62

499-69

•5681

((

“ 600-28

8 689-35

688-85

•7198

4 689-6

901-87

887-82

? 4742-2

4750-48

5-8687

((

188 4760-0

901-9

887-86

44 1161-4

1160-94

1-2970

((

44 1161-4

In the above determinations the coils were arranged in the way as
indicated in the figure having leads of double bell wire.

A Sbhibb or DaTBnin«rjt.TioKB or A Umobr Varioub Consitionb.

Open resistance R on table (original position).

Ooils.

Oorrec.

Queen. E+r.

Oor--

reo.

Avei>

agre.

Com.

A'. Ratio.

902-0

-14-65

887-46 U9+$ 4776-5

-•62

4786-58

1 5-8986

“ 196 -fs 4818-

«t

901-95

887-4 ? 4788-6

4795-88

1 6-408

“ 190+« 4808-6

Open resistance R moved up to coil A (6i).

tt V ?

((

? 4618-

4517-88

2 6-0906

Open resistance R moved to the other side of A (b^.

144 +« 4518-

4618*88

1 5-0922

tt tt 4521*

Coil A placed in Ft

position and open resistance R restored to its

position, and 169' of double wire added to the circuit.

Cor-

Aver-

Coxa.

Coils.

II'',

Corroo,

Queen. B-hr.

reo.

affo.

A'. Ratio.

901-95

-14-65

887*4 647- -f 4129

--62

647

4676

4098-88

2 6-2888

688 H- 4129

583

4713

Coil A at end of double wire 69' + 169' = 828' long.

i< <> « « 007 + 4130

(t c( « ti 607

4736
084 + 4129
034

4768

Few leads placed in Jit circuit, the wires were about 6" from each
other.

832

Hbnbt a. Eowlasto

Colls.

R".

Correo.

Queen. R+r.

902*6

—14*56

888*05 669 + 4129

569

4698

594 + 4129

594

Cor- Com.

reo. Average. A'. Batlo.

4709*88 1 5*8088

4728

Open resistance placed next Coil A.

“ U 668 + 4129

668

“ “ 4292

4791*8 1 5*8956

4292* 2

•7

0*6

In the follo’wing all connectione were made with open leads, and open
resistances were used.

Pe-

Cor-

Aver-

Com.

riod.

Coils.

Correo.

Queen.

R+r.

reo.

age.

A'.

Ratio.

902*

887*45

90 + 8

603*07

-*62

602*71

•6664

90 + 8

608*6

188

((

88 + 8

522*58

((

88 + 8

602*16

601*72

•6668

902 56

888*

17 + 8

644*8

((

18 + 8

644*76

648*91

•7351

188

17+8

648*05

((

17 + 8

648*1

642*46

•7284

902*4

887*85

38 + 8

1159*6

((

38 + 8

1169*1

1168*78

1-8060

188

34 + 8

1167*0

((

36 + 8

1158*8

1167*28

1-8034

C + Pj

902*

887 46

105 + 8

1668*8

((

110 + 8

1664*1

1660*77

1-8718

188

((

101+8

1666*7

((

106 + 8

1660*8

1667*96

1-8689

C + Pa

902*5

887*96

10 + 8

1808*0

13 + 8

1805*0

1808*8

2-0361

138

((

8 + 8

1800*6

((

8+8

1800*2

1799*65

2-0321

p.+p.

902*4

887*85

60 + 8

2806*8

3807*98

3*6995

((

2310*9

138

((

66+8

2804*1

3804*18

3-6961

((

57 + 8

2805*4

902*48

887*88

85 + 8

4708*

106 + 8

4734*3

4713*98

5-8080

138

((

902*4

887*86

83+8

4704*2

({

86 + 8

4707*0

4704*98

6-2091

A + C

902-86

887*8

1146 + 8

9149*6

— 2M

1337 + 8

9388*5

9190*88

10-3615

188

903*4

887*85 1170 +«

9171*7

1104 + 8

9191*7

9181*08

10-3396

• A + C

902*86

887*8

111+8

2650*9

+ 2M

146 + 8

3566*4

2568*08

3-8716

188

88 + 8

2648*7

88 + 8

2648*7

2548*08

3-8701

A + C

902*6

888*06

128

5862*

169

5898*

6880*13

6-6225

138

184

6868*5

(»

140

6869*

5866*68

6-6054

EIiEOTSIOAL Measttbbubkis

333

The above results show to what accuracy self-iuductances of dlf ereut
values can be compared to each other, or to one of the self-inductances
taken as a standard. The reason that the' agreement between the
different determinations is not greater than it is, even though the elec-
trodynamometer was sensitive to a change of 1 part in 10000 in 5 -f- r,
is that there was always some little heating of the resistances, and
although they were measured in each determination on a Wheatstone
bridge, still it was impossible to determine the exact resistance at the
time that the experiment was made. This slight effect of the heating
of the resistance would not enter in the comparison of two nearly equal
self-inductances, that is the comparison of a coil with a standard. The
accuracy of this comparison can be made to depend on the accuracy
with which R-\-r can be determined for zero deflection, and this can
be done to about 1 part in 10000. To do this, first the standard coil
and the coil to be compared are substituted in turn in place of L in
figure; they arc thus compared separately to a third coil. But as the
standard and the coil to be compared are nearly equal in self-inductance,
the difference or self-inductance can be determined by the amount
necessary to change jR-\-r, and this change will be nearly iudependent
of the slight heating of the resistances. To make a coil of the same
self-inductance as the standard, the standard is placed in the B-\-r
circuit and the value of 22 + r is found that produces no deflection.
The coil to bo compared is then substituted in place of the standard
keeping 22 + r fixed, and the self-inductance of this coil is changed
until there is no deflection, as in the case of the standard. The
accuracy with which this can be done depends on the accuracy with
which 22 r can be set or 1 part in 10000. The method therefore
gives a means of comparing and constructing coils to agree in self-
inductance to within 1 part in 10000 with a standard.

Method 6. — Zero Method for the Comparison of Belf-Indnctanee wiHh

Capacity

This method resembles method 12 and the connections are made as
in the figures when both the hanging coil and fixed coils of the electro-
dynamometer arc shunted off the main circuit.

TiCt the currents he denoted by 0',e«C“+*«>, (7,e<(w+«,

and The resistance by 22", /, R and r. The capacity by 0.

The solf-inductancc by L. A' and A" are reversing commutators and
F the terminals of the fixed coils and H the terminals of the hanging
coil of the elcctrodynamomcter.

334

JECbNBT a. BowiiJTD

If new a peiiodic electromotiTe force is applied to the terminals A
and B the equations connecting the difEerent currents are as below,
from which equations the quantity 0^0^ cos (^i — <f>,) is to be found,
which is proportional to the deflection. From the flgure

Ctem+*4) r> = ,

(7^et(w-*4) _ o^m _

Fig. 9.

In the same way it is f otind that

= (?,e< W-*.) 3±L'^}P.^. ,

(iJ"+r')r+j£

Therefore the real part is

(.B+r)(.B"+/)r/ — — rr'

0,0, cos («, - ^.) = 01 o: 1) ,

(i2"+r')‘r-+

ELEOISIOAL MEAStTBEHBNTS

335

where D is -the deflection. "When D is equal to zero

(i2+r)(E"+r') — ^ = 0

.A=(Ji:"+r')(i2+r).

In the experiments by this method the i microfarad Elliott condenser
was used, and it was compared with the different coils Pj, A, and 0.
The connections were made with open leads and open resistances were
used as far as possible, but it was necessary to use resistance boxes for
the last adjustments. The connections having been made as in flgure,
the process of experimenting was to keep r and / constant and to
adjust P" and B until there was no deflection of the hanging coiL The
resistance of the circuits B" + t' and P + *■ 'were then measured on a
Wheatstone bridge. The commutator A' was reversed and the process
was repeated. The condenser had absorption (see p. 3S3) which caused
the resistance P" + ^ to ^6 increased by t - 11 ohms. When the capac-
ity is calculated, taking into account the absorption, it is called the
corrected capacity, as in the other tables of the paper.

OoliLBOTBO KBBCLTS.

Coils.

{(

((

Pi + Pa

0 + Pj
ti

C + P,

C + Px + Pfl
A + C

Results found Results found

nniO. by taking by direot naslSS.

Bosults found sum ditf., em., zneas. of coils Itesults found by taking sum
by direot of separate and ooxnblnatlon and dlH. of separate

measurement. meas. of colls. moasurements.

•5664

-5668

-5784

-5658

-7251

•7211

-7282

•7288

1-8050

1-8049

1-8010

1-8070

1-8084

5-8080

5-8175

1-2945

1-2915

5-2091

1-8718

1*8714

1-8744

1-8688

2-0261

2-0881

2-0221

2-5995

2-5965

2-5951

6-6225

6-6180

6-6054

•5648 (O+Pil— OssPj

•5780 (O+Pi + Pj)— (0 + P9)=Pi

•7187 (O+P*)— OssP*

•7269 (O + Pi + Pj,)— (C + Pi)=P9
1-8029 (0 + Pi)— 1*1=0
1-2990 (C-fP.)— P9=C
1-8065 (O-l-Pi + Pa)— Pi— Pa=0

5- 8022 (A + O— C=A

1-2917 (O + l’j + Pa)— 0=Pi + P*
1-2888 Pj + Ps

1-8677 O + Pj

1- 8718 (0 + Pi + P9)-P*=0 + Pi

2- 0298 (0 + Px + P*)— Pi=0 + P 9

2-5920 P 1 + P 9 + O

6 - 6025 A + C = A - l-0

In method 12 corrections due to the hanging coil and fixed coils were
calculated so that the ratio of the resistances would give the ratio of the
self-inductances direct. In this method (6) since the capacity was in
circuit with the hanging coil, the self -inductance was so small that it
was neglected. The self-inductance of the coils P, etc., which were
joined in circuit with the fixed coils, were increased by the self-induc-
tance of the fixed coils, that is by •0164 henry.

836

. HainiT A. BomiAaiD

The table belo-w gives the various results.

Queen In

Position

ourrent with

Oor.

Coll.

R"+r.

R+r.

Product. A'.

•7261

2008*

206-

1096-7

2198522- 1

•0164

•8878

2005*

200-

•7416

18S

2024-5

221-

2218792- 1

•7228

2025-5

222-

•0164

•8880

*8828

•7897

12741-5

80-

1241-86

15922894- 1

6-8080

80-

•0164

•8844

6-8S44 -

188

12720-

286-

15776610- 1

6-2991

12716-

220-

•0164

-8868

6-8156

8480-8

98-

1140-8

8911004- 1

1-8060

8425-8

98-

•0164

•8879

1-8214

188

8448-8

106 + «

1140-8

8988854- 1

1-8084

8447-0

106 + «

•0164

•8866

•3Sl6

1-8198

1678-5

57 + «

1088-9

1718719-7 1

•8668

1678-4

58 4“ «

•0164

•8884

-6817

This method can be used with great accuracy for the comparison of
the capacity of a condenser with a standard condenser. In the com-
parison, first one condenser and then the other would be placed in the
B-\-r circuit. If the two condensers are of nearly the same capacity,
the degree of accuracy of the comparison depends upon the accuracy
with which 2?" -j- / can be set. The degree of accuracy of setting
JB" r' varies with the value of the self-inductance with which the
condensers are compared. In the experiments just given, using the
different coils, the degree of accuracy with which two ^ microfarad con-
densers could have been compared would vary from 1 part in 2000 to
one part in 14000. The two condensers are supposed to be without
absorption, as its presence would cause trouble unless the absorption
resistances were known.

ELBOTrjOAi. Measttbehekis

337

Bisvme . — Smaming up the results deduced in this paper, it is seen,
that the methods for the absolute determination of self-inductance
and capacity do not gire as concordant results as could he wished. The
irregularity of results was caused, in the most part, both in the deter-
mination of self-inductance and capacity by the variation of the periods
of the currents used in the experiments. As the period enters directly
into the determination of self -inductance and capacity, all variations
of the period will appear in the results. The determination of capacity
is complicated by the presence of electric absorption (p. 333 ei seq.).
The effect of electric absorption is shown to be that of an added resist-
ance in series with the condenser, called absorption resistance. A
direct method is given by which absorption resistance can be measured
(p. 319), and experiments are given which show that when condensers
possessing absorption are in series or in parallel, their absorption re-
sistances act tmder these conditions as oh^c resistances in series with
the separate condensers (p. 333). Absorption resistance is also found
to be extremely sensitive to temperature.

The methods for the comparison of two self-inductances or a self-
inductance and a capacity are independent of the period, and when the
self-inductances are of different magnitudes the comparison can be
made with an accuracy of 1 part in 10000. These methods, therefore,
give a means of comparison of a self-inductance with a standard self-
inductance, or a capacity with a standard capacity to an accuracy of 1
part in 10000, or they allow the establishment of standards.

EESISTANCE TO ETHEREAL MOTION

Bt H. a.. Rowland, N. E. Gilbbbt and P. 0. MoJunokin
yoihm SopkiM University Circulars^ No, 146, p. 60, 1900]

An attempt has been made to determine within w-hat limits it is
possible to say that there is no frictional or viscous resistance in the
ether of space. Modem theories of magnetism are based on some kind
of rotary or vortical motion in the ether and if a piece of iron is mag-
netized we imagine that the molecules, or something about them, rotate
also.' The existence of permanent magnets shows that any retardation
due to any kmd of resistance must be very slight.

In the case of an electro-magnet, any energy used in overcoming such
resistance, if it exists, must be derived from the exciting current and
the disappearance of such energy will produce an apparent resistance
added to that of the wire. An attempt was therefore made to deter-
mine whether a wire carrying a current had the same electrical resist-
ance when producing a magnetic field that it had when not producing it.

The experiment consisted in winding two coils of wire together on
an iron core and determining whether the resistance was the same in
two cases : —

(1). When the current was so passed through the coils that both
produced a field in the same direction.

(13). When the current was so passed that the fields produced counter-
balanced each other.

The great difficulty in the experiment lay in the necessity of measur-
iug the resistance of a coil in which a comparatively large current was
flowing. In order to overcome the effect of changes in resistance due
to changes in temperature, two coils were wound, as nearly as possible
identical, and these double coils were used for the four arms of a
Wheatstone^s bridge so that the temperature would rise in all four arms
equally. Each coil consisted of about 2600 turns of doubled No. 30
copper wire, the whole enclosed m an iron case, boiled in wax for five
hours and cooled in a vacuum. The insulation resistance was then
about eleven megohms. Iron cores were used and it was found that
the cases effectually protected the coils against sudden changes in tern-

Ebsisiakob to Eihbbbal Moiiob

339

perature due to air currents as veil as serving for yokes to tlie magnets.
A current of one-tenth ampere vas used which insured a hi g h state
of magnetization in the iron when two coils were in series, giving 6000
turns.

The coils were connected in the bridge in such a way that the two
coils in one case formed the opposite arms of the bridge. By means
of a reversing switch the current in one of these cohs could be reversed.
This changed the field which might aflect two opposite arms of the
bridge and thus doubled the defiection. Another switch might have
been inserted in the other pair of arms and thus doubled the defiection
again but errors due to the switches would also have been doubled and
no advantage gained. The switch was carefully constructed with large
copper rode dipping into copper mercury cups but, at best, the inac-
curacies of the switch limited the accuracy of the experiment.

The fine adjustments were made by resistance boxes shunted round
one of the coils. About 15,000 ohms in this shunt balanced the bridge.
A change of one ohm in the shunt gave a defiection of two millimeters
and indicated a change in the resistance of the arm of -nrAwohm. The
whole resistance being over 100 ohms this would give a determination
of one part in 9,000,000 or, since the defiection is doubled, one part in
4,000,000 for each arm. The result of 30 readings each way was that
the shunt resistance was about 3-4 ohms less with magnetic field than
without. The shunt was so placed that this gives a less resistance by
one part in 1,900,000 when producing a magnetic field.

The above result is in the wrong direction. The difficulty may lie in
the fact that the galvanometer, though used at night, was rmsteady at
best, or it may be due to leakage. The resistance of the coils was 100
ohms while the insulation resistance was 11,000,000 ohms. If the leak-
age is symmetrical along the doubled wire it will not affect the galvano-
meter upon reversing the current in one coil. This assumption may
not be jxistifled.

PART III

HEAT

ON THE MECHANICAL EQUIVALENT OP HEAT, WITH SUB-
SIDIAEY EESEAECHES ON THE VAEIATION OP THE
MEEOUEIAL PEOM THE AIE THEEMOMETEE, AND ON
THE VAEIATION OP THE SPECIFIC HEAT OP WATEE‘

IProctedingt qf the Amtriom Aeoaony of A.rU and Soieneei, XY, 78-200, 1880]

iKyaSTiOATiOHS OK liiOHT AKD Hbat, made and pnbUslied wholly or in part with
appropriation from tlie Bttmfobd Funb

Presented June 11th, 1879

CONTBISTTS

I. Introductory remarks .... 848

II. Thermometry 845

(a.) General view of Thermom-
etry .845

(&.) The Mercurial Thermometer 846
(c.) Kelatlon of the Mercurial

and Air Thermometers 852

1. General and Historical

Remarks .... 852

2. Description of Appa-

ratus 858

8. Results of Comparison 866
(d.) Reduction to the Absolute

Scale 881

Appendix to Thermometry . 884

III. Calorimetry 887

(a.) Specific Heat of Water . 887
(5.) Heat Capacity of the Calo-
rimeter 899

IV. Determination of Equivalent . 404

(a.) Historical Remarks . . . 404

1. General Review of

Methods 405

2. Results of Best Deter-

minations .... 409
(5.) Description of Apparatus 422

1. Preliminary Remarks . 422

2. General Description . 424

8. Details 426

1. Estimation of Work

Done 480

2. Radiation 486

8. Corrections to Ther-
mometers, etc. . . 489

(d.) Results 1 441

1. Constant Data . . . 441

2. Experimental Data and

Tables of Results . 441
V. Concluding Remarks and Criti-
cism of Results and Methods 465

I.— INTRODUCTORY REMARKS

Among the more important constants of nature, the ratio of the
heat unit to the unit of mechanical work stands forth prominent, and

1 This research was originally to have been performed In connection with Professor
Pickering, but the plan was frustrated by the great distance between our residences.
An appropriation for this experiment was made by the American Academy of Arts
and Sciences at Boston, from the fund which was instituted by Count Rumford, and
liberal aid was also given by the Trustees of the Johns Hopkins University, who are
desirous, as far as they can, to promote original scientific Investigations.

344:

Hbney a. Eowland

is used almost daily by the physicist. Yet, when we come to consider
the history of the subject carefully, we find that the only experimenter
who has made the determination with anything like the accuracy
demanded by modem science, and by a method capable of giving good
results, is Joule, whose determination of thirty years ago, confirmed
by some recent results, to-day stands almost, i£ not quite, alone among
accurate results on the subject.

But Joule experimented on water of one temperature only, and did
not reduce his results to the air thermometer; so that we are still left
in doubt, even to the extent of one per cent, as to the value of the
equivalent on the air thermometer.

The reduction of the mercurial to the air thermometer, and thence
to the absolute scale, has generally been neglected between 0® and 100®
by most physicists, though it is known that they diflEer several tenths
of a degree at the 45® point. In calorimetric researches this may pro-
duce an error of over one, and even approaching two per cent, especially
when a Q-eissler thermometer is used, which is the worst in this respect
of any that I have experimented on; and small intervals on the mer-
curial thermometers differ among themselves more than one per cent
from the difference of the glass used in them.

Again, as water is necessarily the liquid used in calorimeters, its
variation of specific heat with the temperature is a very important
factor in the determination of the equivalent. Strange as it may
appear, we may be said to know almost nothing about the variation
of the specific heat of water with the temperature betw6en 0® and
100® C.

Eegnault experimented only above 100® C. The experiments of
Him, and of Jamin and Amaury, are absurd, from the amount of varia-
tion which they give. Pfaundler and Platter confined themselves to
points between 0® and 13®. Munchausen seems to have made the best
experiments, but. they must be rejected because he did not reduce to
the air thermometer. • ■

In the present series of researches, I have sought, first, a method
of measuring temperatures on the perfect gas thermometer with an
accuracy scarcely hitherto*" attempted, and to this end have made an
extended study of the deviation of ordinary thermometers from the
air thermometer; and, secondly, I have sought a method of determin-
ing the mechanical equivalent of heat so accurate, and of so extended
a range, that the variation of the specific heat of water should follow
from the experiments alone.

On xhb Mbohanioal Bquivalbnt of Heat

346

As to whether or not these have heen accomplished, the following
pages will show. The cnrions result that the specific heat of water
on the mr thermometer decreases from 0® to about 30® or 35®, after
which it increases, seems to he an entirely unique fact in nature, seeing
that there is apparently no other substance hitherto experimented upon
whose specific heat decreases on rise of temperature without change of
state. From a thermodynamic point of view, however, it is of the
same nature as the decrease of specific heat which takes place after
the vaporization of a liquid.

The close agreement of my result at 15® -7 0. with the old result of
Joule, after approximately reducing hie to the air thermometer and
latitude of Baltimore, and correcting the specific heat of copper, is
very satisfactory to us both, as the difference is not greater than 1 in
400, and is probably less.

I hope at some future time to make a comparison with Joule’s ther-
mometers, when the difference can be accurately stated.

U.— THBEMOMBTRT
(«.) General View

The science of thermometry, as ordinarily studied, is based upon
the changes produced in bodies by heat. Among these we may mention
change in volume, pressure, state of aggregation, dissociation, amount
and color of light reflected, transmitted, or emitted, hardness, pyro-elec-
tric and ihermo-electric properties, electric conductivity or specific in-
duction capacity, magnetic properties, thermo-dynamic properties, &c.;
and on each of these may be based a system of thermometry, each one
of which is perfect in itself, but which differs from all the others widely.
Indeed, each method may be applied to nearly all the bodies in nature,
and hundreds or thousands of thermometric scales may be produced,
which may be made to agree at two fixed points, such as the freezing
and boiling points of water, but which will in general differ at nearly,
if not all, other points.

But from the way in which the science has advanced, it has come
to pass that all methods of thermometry in general use to the present
time have been reduced to two or three, based respectively on the
apparent expansion of mercury in glass and on the absolute expansion of
some gas, and more lately on the second law of thermodynamics.

Bach of these systems is perfectly correct in itself, and we have no
right to designate either of them as incorrect. We must decide a priori

34:6

Hbnut a. Eowlaot)

on some system, aad then express all our results in that system: the
accuracy of science demands that there should be no ambiguity on that
subject. In deciding among the three systems, we should be guided
by the following rules: —

1st. The system should be perfectly definite, so that the same tem-
perature should be indicated, whatever the thermometer.

2d. The system should lead to the most simple laws in nature.

Sir William Thomson's absolute system of thermometry, coinciding
with that based on the expansion of a perfect gas, satisfies these most
nearly. The mercurial thermometer is not de^te unless the kind of
glass is given, and even then it may vary according to the way the bulb
is blown. The gas thermometer, unless the kind of gas is given, is not
definite. And, further, if the temperature as given by either of these
thermometers was introduced into the equations of thermo-dynamics,
the simplest of them would immediately become complicated.

Throughout a small range of temperature, these systems agree more
or less completely, and it is the habit even with many eminent physi-
cists to regard them as coincident between the freezing and boiling
points of water. We shall see, however, that the difference between
them is of the highest importance in thermometry, especially where
differences of temperature are to be used.

Tor these reasons I have reduced all my measures to the absolute
system.

The relation between the absolute system and the system based on
the expansion of gases has been determined by Joule and Thomson
in their experiments on the flow of gases through porous plugs (Philo-
sophical Transactions for 1862, p. 679). Air was one of the most
important substances they experimented upon.

To measure temperature on the absolute scale, we have thus only to
determine the temperature on the air thermometer, and then reduce
to the absolute scale. But as the air thermometer is very inconvenient
to use, it is generally more convenient to use a mercurial thermometer
which has been compared with the air thermometer. Also, for small
changes of temperature the air thermometer is not sufficiently sensi-
tive, and a mercurial thermometer is necessary for interpolation. I shall
occupy myself first with a careful study of the mercurial thermometer.

(6.) The Mercurial Thermometer

Of the two kinds of mercurial thermometers, the weight thermometer
is of little importance to our subject. I shall therefore confine myself

On thh Mbobcanioal Equitalbni ov Heat

347

principally to that form having a graduated stem. For convenience
in nse and in calibration, the principal hulh should be elongated, and
another small bulb should be blown at the top. This latter is also of
the utmost importance to the accuracy of the instrument, and is placed
there by nearly aH makers of standards.’ It is used to place some of
the mercury in while calibrating, as well as when a high temperature
is to be measured; also, the mercury in the larger bulb can be made
free from air-bubbles by its means.

Host standard thermometers are graduated to degrees; but Begnault
preferred to have his thermometers graduated to parts of equal capacity
whose value was arbitrary, and others have used a single millimeter
division. As thermometers change with age, the last two methods are
the best; and of ihe two I prefer the latter where the highest accuracy
is desired, seeing that it leaves less to the maker and more to the
scientist. The cross-section of the tube changes continuously from
point to point, and therefore the distribution of marks on the tube
should be continuous, which would involve a change of the dividing
engine for each division. But as the maker divides his tube, he only
changes the length of his divisions every now and then, so as to average
his errors. This gives a sufficiently exact graduation for large ranges
of temperature; but for small, great errors may be introduced. Where
there is an arbitrary scale of millimeters, I believe it is possible to
calibrate the tube so that the errors shall be less than can be seen with
the naked eye, and that the table foxmd shall represent very exactly
the gradual variation of the tube.

In the calibration of my thermometers with the millimetric scale, I
have used several methods, all of which are based upon some graphical
method. The first, which gives all the irregixlarities of tho tube with
great exactness, is as follows:

A portion of the mercury having been put in the upper bulb, so as
to leave tho tube free, a column about 16 mm. long is separated oft.
This is moved from point to point of the tube, and its length carefully
measured on tho dividing engine. It is not generally necessary to
move the column its own length every time, but it may be moved
30 mm. or 36 mm., a record of the position of its centre being kept.
To eliminate any errors of division or of the dividing engine, readings
were then taken on the scale, and the lengths reduced to their value
in scale divisions. The area of the tube at every point is inversely as

< Oelsslor and Casolla omit it, which should condemn their thermometers.

348

Hbnbt a. Eowlaito

the len^h of the coh inm . shall thus haye a series of fibres nearly
equal to each other, if the tube is good. By subtractiag the smallest
from each of the others, and plotting the results as ordinates, with the
thermometer scale as abscissas, and drawing a curve through the points
so found, we have means of finding the area at any point. The curve
should not be drawn exactly through the points, but rather around
them, seeiog they are the average areas for some distance each side of
the point. With good judgment, the curve can be drawn with great
accuracy. I then draw ordinates every 10 mm., and estimate the aver-
age areia of the tube for that distance, which I set down in a table.
As the lengths are uniform, the volume of the tube to any point is
found by adding up the areas to that point.

But it would be unwise to trust such a method for very long tubes,
seeing the mercury column is so short, and the columns are not end to
end. Hence I use it only as supplementary to one where the column
is about 60 mm. long, and is always moved its own length. This estab-
lishes the volumes to a series of points about 60 -nmin. apart, and the
other table is only used to interpolate in this one. There seems to be
no practical object in using columns longer than this.

Having finally constructed the arbitrary table of volumes, I then
test it by reading with the eye the length of a long mercury column.
Ho certain error was thus found at any point of any of the thermom-
eters which I have used in these experiments.

While measuring the column, great care must be taken to preserve
all parts of the tube at a uniform temperature, and only the extreme
ends must be touched with the hands, which should be covered with
cloth.

If F is the volume on this arbitrary scale, the temperature on the
mercurial thermometer is found from the formula T = OV — where
0 and #0 are constants to be determined. If the thermometer contains
the 0“ and 100° points, we have simply

Xoc-K''

Otherwise 0 is found by comparison with some other thermometer,
which must be of the same kind of glass.

It is to be carefully noted that the temperature on the mercurial
thermometer, as I have defined it, is proportional to the apparent ex-
pansion of mercury as measured on the stem. By defining it as pro-
portional to the true volume of mercury in the stem, we have to intro-
duce a correction to ordinary thermometers, as Poggendorff has shown.

On the Mbohanioal Equivalent oe Heat

349

As I only use the mercurial thermometer to compare mth the air
thermometer, and as either definition is equally correct, I vill not
further discuss the matter, hut will use the first definition, as being
the simplest.

In the above formula I have implicitly assumed that the apparent
expansion is only a function of the temperature; but in solid bodies
like glass there seems to be a progressive change in the volmne as time
advances, and especially after it has been heated. And hence in mer-
curial and alcohol thermometers, and probably in general in all ther-
mometers which depend more or less on the expansion of solid bodies,
we find that the reading of the thermometer depends, not only on its
present temperature, but also on that to which it has been subjected
within a short time; so that, on heating a thermometer up to a certain
temperature, it does not stand at the same point as if it had been cooled
from a higher temperature to the given temperature. As these effects
are without doubt due to the glass envelope, we might greatly diminish
them by using thermometers filled with liquids which expand more
than mercury: there are many of these which expand six or eight times
as much, and so the irregularity might be diminished in this ratio. But
in this case we should find that the correction for that part of the
stem which was outside the vessel whose temperature we were deter-
mining would be increased in the same proportion; and besides, as all
the liquids are quite volatile, or at least wot the glass, there would be
an irregularity introduced on that account. A thermometer with liquid
in the bulb and mercury in the stem would obviate these inconven-
iences; but even in this case the stem would have to be calibrated before
the thermometer was made. By a comparison with the air-thermom-
eter, a proper formula could be obtained for finding the temperature.

But I hardly believe that any thermometer superior to the mercurial
can at present be made, — ^that is, any thermometer within the same
compass as a mercurial thermometer, — and I think that the best result
for small ranges of temperature can bo obtained with it by studying
and avoiding all its sources of error.

To judge somewhat of the laws of the change of zero within the
limits of temperature which I wished to use, I took thermometer S’©.
6163, which had lain in its case during four months at an average
temperature of about 30“ or 36“ 0., and observed the zero point, after
heating to various temperatures, with the following result. The time
of heating was only a few minutes, and the zero point was taken imme-

350

HkNBT a. EOTflJJJD

diately after; some fifteen minutes, however, being necessary for the
thermometer to entirely cool.

TABLE I. — SHOW117Q CHA17GB OB' Zbibo Point.

Temperature
of Bulb
before finding
the 0 Point.

Ohangeof

OPoSxt.

Temperature
of Bulb
before finding
the 0 Point.

Ohangeof

OPolnt.

32® 6

70® 0

— 116

80-0

— 016

81-0

— 170

40-5

— 088

90*0

— 381

51-0

— 089

100-0

— 818

60-0

— 106

100-0

—847

The second 100® reading was taken after boiling for some time.

It is seen that the zero point is always lower after heating, and that
in the limi ts of the table the lowering of the zero is about proportional
to the square of the increase of temperature above 25® C. This law
is not true much above 100°, and above a certain temperature the
phenomenon is reversed, and the zero point is higher after heating;
but for the given range it seems qxdte exact.

It is not my purpose to make a complete study of this phenomenon
with a view to correcting the thermometer, although this has been
undertaken by others. But we see from the table that the error can-
not exceed certain limits. The range of temperature which I have
used in each experiment is from 20® to 30® C., and the temperature
rarely rose above 40® 0. The change of zero in this range only amounts
to 0°-03 0..

The exact distribution of the error from this cause throughout the
scale has never been determined, and it affects my results so little that
I have not considered it worth investigating. It seems probable, how-
ever, that the error is distributed throughout the scale. If it were
uniformly distributed, the value of each division would be less than
before by the ratio of the lowering at zero to the temperature to which
the thermometer was heated.

The ma xim u m errors produced in my thermometers by this cause
would thus amount to 1 in 1300 nearly for the 40° thermometer, and
to about 1 in 2000 for the others. Rather than allow for this, it is
better to allow time for the thermometer to resume its original state.

Only a few observations were made upon the rapidity with which
the zero returned to its original position. After heating to 81°, the

On the Mbobcanioal Equivalent oe Heat

351

zero returned from — O'’'1'J'O to — O'-MS in two hours and a half.
After heating to 100®, the zero returned from — 0®-347 to — 0®-110
in nine days, and to — 0°-023 in one month. Eeasoning from this, I
should say that in one week thermometers which had not been heated
above 40° should be ready for use again, the error being then supposed
to be less than 1 in 4000, and this would be partially eliminated by
comparing with the air thermometer at the same intervals as the ther-
mometer is used, or at least heating to 40° one week before comparing
with the air thermometer.

As stated before, when a thermometer is heated to a very high
point, its zero point is raised instead of lowered, and it seems probable
that at some higher point the direction of change is reversed again;
for, after the mstmment comes from the maker, the zero point con-
stantly rises until it may be 0°-6 above the mark on the tube. This
gradual change is of no importance in my experiments, as I only use
differences of temperature, and also as it was almost inappreciable in
my thermometers.

Another source of error in thermometers is that due to the pressure
on ihe bulb. In determining the freezing point, large errors may be
made, amounting to several hundredths of a degree, by the pressure of
pieces of ice. In my experiments, the zero point was determined in
ice, and then the thermometer was immersed in the water of the com-
parator at a depth of about 60 cm. The pressure of this water affected
the thermometer to the extent of about 0°*01, and a correction was
accordingly made. As differences of temperature were only needed,
no correction was made for variation in pressure of the air.

It does, not seem to me well to use thermometers with too small a
stem, as I have no doubt that they are subject to much greater irregu-
larities than those with a coarse bore. For the capillary action always
exerts a pressure on the bulb. Hence, when the mercury rises, the
pressure is due to a rising meniscus which causes greater pressure than
the faUing meniscus. Hence, an apparent friction of the mercurial
column. Also, the capillary constant of mercury seems to depend on
the electric potential of its surface, which may not be constant, and
would thus cause an irregularity.

My own thermometers did not show any apparent action of this kind,
but Pfaundler and Platter mention such an action, though they give
another reason for it.

352

Hbnby a. Rowlaot)

(0.) Relation of the Mercurial and Air Thermometers
1. O-ETNiasLAX Am> Hzstobioal BsiCAnss

Since the time of Dnlong and Petit, many experiments have been
made on the difference between the mercurial and the air thermometer,
but unfortunately most of them have been at high temperatures. As
weight thermometers have been used by some of the best experimenters,
I shall commence by proving that the weight thermometer and stem
thermometer give the same temperature; at the same time, however,
obtaining a convenient formula for the comparison of the air ther-
mometer with the mercurial.

For the expansion of mercury and of glass the following formula
must hold: —

For mercury, F = F (1 + + 5^ + do.) ;

glass. F^ — F^ Q ^1 -j- 4“ “h 5

In both the weight and stem thermometers we must have F = V\

77-/ 77 1 -f- + ^0.

Fo (1 + + &C.).

where F'o and 7o are the volumes of the glass and of the mercury
reduced to zero, and t is the temperature on the air thermometer.
The temperature by the weight thermometer is

® — 1

S ’ =100 §51 = 100 5 —

Jf -L

* 100

where Pq, P , &c., are the weights of mercury in the bulb at 0® C.,
C., &c.

Now these weights are directly as the volumes of the mercury at 0®.

= 1 + -h £1^ + dkc.,

seeing that F is constant.

P=100

+ £^ +

100 A + (100)*P +

In the stem thermometers we have the volume of mercury at 0®,
constant, and the volume of the glass that the mercury fills, reduced
to 0®, variable. As the volume of the glass F'o is the volume reduced
to 0®, it will be proportional to the volume of bulb plus the volume of
the tube as read off on the scale which should be on the tube.

On the Meohanioal Bquitalent of Huat

353

(F'.),., - (7'.). - —

P— 1
0

. /p 1 on _ •AP "I’

. . A _ xuv ;:^- j. jQij-j,- jg ^ -

which is the same as for the weight thermometer.

If the fixed points are 0° and i'® instead of 0® and 100®, we can write
^_^At + Bi? + Gff‘ + &c.

^ - * ir+Bwrvi’^TM.

r=# ji + (<-/') 1^1 + , 0.

^ + &C. I

S’ = < { 1 + (< - i') [f + J #'+^- (^ + i') ] + &o. }

As T and t are nearly equal, and as we shall determine the constants
experimentally, we may write

t = T- at(f - )5) (5 _ <) + &o.,

Where t is the temperature on the air thermometer, and T that on the
mercurial thermometer, and a and "b are constants to be determined for
each thermometer.

The formula might be expanded still further, but I think there are
few cases which it will not represent as it is. Considering b as equal
to 0, a formula is obtained which has been used by others, and from
which some very wrong conclusions have been drawn. In some kinds
of glass there are three points which coincide with the air thermometer,
and it requires at least an equation of the third degree to represent
this.

The three points in which the two thermometers coincide are given
by the roots of the equation

t(t'-t)(b-i) = Q,

and are, therefore.

t = 0

t = b.

In the following discussion of the historical results, I shall take 0®
and 100® as the fixed points. Hence, <' = 100°. To obtain a and 6,
two observations are needed at some points at a distance from 0° and
100°. That wo may got some idea of the values of the constants in
the formula for different kinds of glass, I will discuss some of the
experimental results of Eegnault and others with this in view.

354

Hbnrt a. Eowland

Regnault’s results axe embodied, for the most part, in tables given on
p. 239 of tbe first volume of bis Belation des Expiriences. The figures
given there are obtained from curves drawn to represent the mean of
his experiments, and do not contain any theoretical results. The direct
application of my formula to his experiments could hardly be made with-
out immense labor in finding the most probable value of the constants.

But the following seem to satisfy the experiments quite well; —

Oristal de Ohoisy-le-Roi J = 0,
Verre Ordinaire h = 245°,

Verre Vert h = 2’!'0°,

Verre de Sufide i = +10°,

a = .000 000 32.
a = .000 000 34.
a = .000 000 095
a = .000 000 14.

From these values I have calculated the following: —

TABLB II BnoMiLVLT’s RasuLis Compabbb with tkb Formcla.

Air Thermom.

Oholsy-le-Rol.

Verre Ordinaire.

Verre Vert.

Verre do SuOde.

■ S

-d

*01

100

120

140

160

180

200

220

240

260

280

800

820

840

120-12

140-29

160-52

180-80

201-25

221-82

242-55

268-44

284-48

120-09

140-25

160-49

180-88

201-28

221-86

242-60

268-46

284-52

>*»Av fta

-I- -08
+ •04
+ ■08
— 08
— 08

— 04

— 01
— 02

— 04

— 05
+ -42

119-95

189-85

159-74

179-68

199- 70
219-80
289-90

200- 20
« 280 -58

801-08

821-80

484-00

119-90

139-80

159-72

179-68

199-69

219-78

|289-96

260-21

280-00

801-12

821-80

842-04

+ •05
+ ■06
+ -02
—•05
+ •01
+ •02
— 06
— 01
— 02
— 04
-00
4- -86

120-07

140-21

160-40

180-60

200-80

221-20

241-60

202-15'

282-85

120-09

140-22

160-39

180-62

200-89

221-28

241*68

262-09

282-68

— 01
— 01
+ -01
— 02

— 09
— 08

— 08
+ -07
+ -22

120-04

140-11

100-30

180-88

200-50

220-75

241-16

120-04

140-10

100-21

180-84

200-58

220-78

'241-08

+ •01
—01
— •01
—08
—on
+ •08

OUO- f0,OUO*

837 -26 837 -20
S49-80|848-88

The formula, as we see from the table, represents all Regnault’s
curves with great aceuraey, and if we turn to his experimental results
we shall fibad that the deviation is far within the limits of the experi-
mental errors. The greatest deviation happens at 340°, and may be
accounted for by an error in drawing the curve, as there are few experi-
mental results so high as this, and the formula seems to agree with
them almost as well as Regnault’s own curve.

3 Corrected from S380«63 in Uegnault’s table.

On tub MeohanicaIi Equivalent oe Heat

356

The object of comparing the formula with Eegnault’s results at
temperatures so much higher than I need, is simply to test the formula
through as great a range of temperatures, and for as many kinds of
glass, as possible. If it agrees reasonably well throughout a great
range, it will probably be very accurate for a small range, provided
we obtain the constants to represent that small range the best.

Having obtained a formula to represent any series of experiments,
we can hardly expect it to hold for points outside our series, or even
for interpolating between experiments too far apart, as, very often, a
small change in one of the constants may affect the part we have not
experimented on in a very marked manner. Thus in applying the
formula to points between 0“ and 100“ the value of 6 will affect the
result very much. In the case of the glass Choisy-le-Roi many values
of i will satisfy the observations besides l — O. For the ordinary
glass, however, i is well determined, and the formula is of more value
between 0“ and 100“.

The following table gives the results of the calculation.

TABLE III. — Rbonault’8 Kbbults Compabbd with the Eokmula.

100

Calculated
a»*(X)0000 82
5-0.

ChoIsy-le-KoI.

Calculated
a-“(XX)U00 34
5-845.

Observed.

Oaloulated
a -'000 000 44
5-m

Verre

Ordinaire.

Vorro

Ordinaire.

Verre

OrcUnairo.

10-00

10-07

10-10

19-99

20-12

20- 17

29-98

80-15

80-12

+ -08

80-21

+ -09

89-97

40-17

40-28

— 00

40-28

49-90

50-17

50-28

— 00

50-28

59-95

00-15

00-24

— 09

00-21

— 08

09-95

70-12

70-22

— 10

70-18

— 04

79-90

80-09

80-10

— 01

80-11

+ *01

89-97

90-05

90-07

TOO

100

Kegnault does not seem to have puhlished any experiments on Choisy-
le-Roi glass between 0® and 300®, but in tlio tabic between pp. 226, 227,
there are some results for ordinary glass. The separate observations
do not seem to have been very good, but by combining the total number
of observations I have found the results given above. Tlio numbers in
the fourth cohimn are found by taking the mean of Rognault’s results
for points as near the given temperature as possible. The agreement

356

Bjinet a. Eowlajstd

is oiily fair, but we must remember tbat the same specimens of glass
were not used in this experiment as in the others, and that for these
specimens the agreement is also poor above 100°. The values a =
.000,000,44 and 5 = 260° are much better for these specimens, and
the seventh column contains the values calculated from these values.
These values also satisfy the observations above 100° for the given
specimens.

The table seems to show that between 0° and 100° a thermometer of
Choisy-le-Eoi almost exactly agrees with the air thermometer. But
this is not at all conclusive. Eegnanlt, however, remarks,* that be-
tween 0° and 100° thermometers of this glass agree more nearly with
the air thermometer than those of ordinary glass, though he states
the diEEerence to amount to *1 to -2 of a degree, the mercurial ther-
mometer standing ielow the air thermometer. With the exception of
this remark of Eegnault^s, no experiments have ever been published
in which the direction of the deviation was similar to this. All ex-
periments have found the mercurial thermometer to stand dbova the
air thermometer between 0° and 100°, and my own experiments agree
with this. However, no general rule for all kinds of glass can be
laid down.

Boscha has given an excellent study of Eegnault^s results on this
subject, though I cannot agree with all his conclusions on this subject.
In discussing the difiEerence between 0° and 100° he uses a formula of
the form

and dednceB from it the erroneoiiB conclusion that the difference is
greatest at 60° 0., instead of hetiireen 40“ and 50“ . His results for

T — i at 60“ are

Choisy-le-Eoi — -32

Terre Ordinaire -[-.35

Terre Tert +.14

Terre de Su^de +-R6

and these are probably somewhat nearly correct, except the negative
value for Ohoisy-le-Eoi.

With the exception of Eegnanlt, very few observers have taken tip
this subject. Among these, however, we may mention Eccknagel, who

* Oomptes Rendus, Ixix.

On thb Mbohanioal E^xtitalent oi Hbat

357

has made the determination for common glass between 0° and 100°.
I have found approximately the constants for my formula in this case,
and have calculated the values in the fourth column of the following
table.

table IV. — BBaKNjLaiiL’s Bbbclts Oompabbs wiTn thb EoBUirLiL..

_ Air
Thermomoter.

Morourlal T

Observed.

hiormoDaotor.

Calculated.

Blfferonoe.

10-08

20-14

80-18

40-20

50-20

60-18

70-14

70-15

+ -01

80-10

80-11

+ •01

90-05

90-06

+ •01

100

100-00

J = a90°, <* = .000 000 33,

T= i+af (100

It will be seen that the values of the constants are not very diflEerent
from those which satisfy Eegnault’s experiments.

There seems to be no doubt, from all the experiments we have now
discussed, that the point of maximum difiEerence is not at 60°, but at
some less temperature, as 40° to 46°, and this agrees with my own
experiments, and a recent statement by Ellis in the Philosophical
Magazine. And I think the discussion has proved beyond doubt that
the formula is sufBciently accurate to express the difference of the
mercurial and air thermometers throughout at least a range of 200°,
and hence is probably very accurate for the range of only 100° between
0° and 100°.

Hence it is only necessary to find the constants for my thermometers.
But before doing this it will be well to see how exact the comparison
must be. As the thermometers are to be used in a calorimetric research
in which differences of temperature enter, the error of the mercurial
compared with the air thermometer will be

- 1 = a {W — 3 (5+0 <+a^*K

358

Henbt a. Rowland

which for the constants used in Eecknagel’s table becomes
Error = ^ — 1 = .000 000 33 { 29000 — 780i +Bt*\.

This amounts to nearly one per cent at 0°, and thence decreases to
45°, after which it increases again. As only 0°-2 at the 40° point
produces this large error at 0°, it follows that an error of only 0°*02
at 40° will produce an error of -nyVir at 0°. At other points the errors
will be less.

Hence extreme care must be taken in the comparison and the most
accurate apparatus must be constructed for the purpose.

2. Desckiptioit of Apparatus
The Air Thennometer

In designing the apparatus, I have had in view the production of
a uniform temperature combined with ease of reading the thermom-
eters, which must be totally immersed in the water. The uniformity,
however, needed only to apply to the air thermometer and to the bulbs
of the mercurial thermometer, as a slight variation in the temperature
of the stems is of no consequence. A uniform temperature for the air
thermometer is important, because it must take time for a mass of air
to heat up to a given temperature within 0°*01 or less.

Fig. 1 gives a section of the apparatus. This consists of a large
copper vessel, nickel-plated on the outside, with double walls an inch
apart, and made in two parts, so that it could be put together water-
tight along the line ah. As seen from the dimensions, it required
about 28 kilogrammes of water to fill it. Inside of this was the vessel
m d ef ghTcln^ which could be separated along the line d h. In the
upper part of this vessel, a piston, g, worked, and could draw the water
from the vessel. The top was closed by a loose piece of metal, o p,
which fell down and acted as a valve. The bottom of this inner
vessel had a false bottom, c I, above which was a row of large holes ;
above these was a perforated diaphragm, s. The bulb of the air ther-
mometer was at t, with the bulbs of the mercurial thennometers almost
touching it. The air thermometer bulb was very much elongated, being
about 18 cm. long and 3 to 5 cm. in diameter. Although the bulbs of
the thermometers were in the inner vessel, the stems wore in the
outer one, and the reading was accomplished through the thick glass
window u v.

On the Mechanical Equivalent of Heat

359

The change of the temperature was ejflEected by means of a Bunsen
burner under the vessel w.

The working of the apparatus was as follows: The temperature
having been raised to the required point, the piston q was worked to
stir up the water; this it did by drawing the water through the holes

at ol and the perforated diaphragm a, and thence up through the
apparatus to return on the outside. When the whole of the water is
at a nearly uniform temperature the stirring is stopped, the valve o p
falls into place, and the connection of the water in the outer and inner
vessels is practically closed as far as currents are concerned, and be-
fore the water inside can cool a little the outer water must have cooled
considerably.

360

BEbnet a. ’Rgwlajhd

So effective was tliis arrangement that, although some of the ther-
mometers read to 0®*007 0., yet they would remain perfectly stationary
for several minutes, even when at 40® 0. At very high temperatures,
such as 80® or 90® C., the burner was kept under the vessel w all the
time, and supplied the loss of the outer vessel by radiation. The inner
vessel would under these circumstances remain at a very constant tem-
perature. The water in the outer vessel never differed by more than
a small fraction of a degree from that in the inner one.

To get the 0® and 100® points the upper parts of the vessel above
the line a I were removed, and ice placed around the bulb of the air
thermometer, and left for several hours, until no further lowering took
place. For the 100® point the copper vessel shown in Fig. 3 was used.
The portion y of this vessel fitted directly over the bulb of the air
thermometer. On boiling water in a?, the steam passed through the
tube to the air thermometer. It is with considerable difficulty that
the 100® point is accurately reached, and, unless care be taken, the
bulb will be at a slightly lower temperature. Not only must the bulb be
in the steam, but the walls of the cavity must also be at 100®. To
accomplish this in this case, a large mass of cloth was heaped over the
instrument, and then the water in a? vigorously boiled for an hour or so.
After fifteen minutes there was generally no perceptible increase of
temperature, though an hour was allowed so as to make certain.

The external appearance of the apparatus is seen in Fig. 2. The
method of measuring the pressure was in some respects similar to that
used in the air thermometer of Jolly, except that the reading was taken
by a cathetometer rather than by a scale on a mirror. The capillary
stem of the air thermometer leaves the water vessel at a, and passes
to the tube 5, which is joined to the three-way cock c. The lower part
of the cock is joined by a rubber tube to another glass tube at d, which
can be raised and lowered to any extent, and has also a fine adjustment.
These tubes were about 1-6 cm. diameter on the inside, so that there
should be little or no error from capillarity. Both tubes were toctly
of the same size, and for a similar reason.

The three-way cock is used to fill the apparatus with dry air, and
also to determine the capacity of the tube above a given mark. In
filling the bulb, the air was pumped out about twenty times, and
allowed to enter through tubes containing chloride of calcium, sulphuric
acid, and caustic soda, so as to absorb the water and the carbonic acid.

On THB MEOHANIOAL iQinVALENI OE Hbai

361

The Cathetometer

Tlie cathetometer was one made by Meyerst^, and was selected
becanse of the form of slide used. The support was round, and the
telescope was attached to a sleeve which exactly fitted the support.
The greatest error of cathetometers arises from the upright support
not being exactly true, so that the telescope will not remain in level
at all heights. It is true that the level should be constantly adjusted,
but it is also true that an instrument can be made where such an ad-
justment is not necessary. And where time is an element in the
accuracy, such an instrument should be used. In the present case it
was absolutely necessary to read as quickly as possible, so as not to

leave time for the column to change. In the first place the rotmd
column, when made, was turned in a lathe to nearly its final dimen-
sions. The line joining the centres of the sections must then have
been very accurately straight. In the subsequent fitting some slight
irregularities must have boon introduced, but they could not have been
great with good workmanship.* The upright column was fixed, and
the telescope moved around it by a sleeve on the other sleeve. Where
the objects to be measured are not situated at a very wide angle from
each other, this is a good arrangement, and has the advantage that any
side of the column can be turned toward the object, and so, even if it

® The change of level along the portion generally need did not amount to more
than -1 of a division, or about 'Olmm. at the mercury column, as this is about the
smallest quantity vrhlch could be observed on the level.

Henet a. Eowland

were crooked, we could yet turn, it into such a position as to nearly
eliminate error.

It was used at a distance of about 110 cm. from the object, and no
difl&culty was found after practice in setting it on the column to mm.
at least. The cross hairs made an angle of 45® with the horizontal, as
this, was found to be the most sensitive arrangement.

The scale was carefully calibrated, and the relative errors® for the
portion used were determined for every centimeter, the portion of the
scale between the 0® and 100® points of the air thermometer being
assumed correct. There is no object in determining the absolute value
of the scale, but it should agree reasonably well with that on the
barometer ; for let and J?ioo be the readings of the barometer,

and Ro, hp and the readings of the cathetometer at the temperatures
denoted by the subscript. Then approximately

t = — {Eq + Rq) _ Ef — Eq + Rt — Rq

“H Rioo) (,E(^ + Rq) Eiqq Eq 4“ Rioo ^

As the height of the barometer varies only very slightly during an
experiment, the value of this expression is very nearly

ht Rq
^^loo Ro

which does not depend on the absolute value of the scale divisions.

But the best manner of testing a cathetometer is to take readings
upon an accurate scale placed near the mercury columns to be meas-
ured. I tried this with my instrument, and found that it agreed with
the scale to within two or three one-hundredths of a millimeter, which
was as near as I could read on such an object.

In conclusion, every care was taken to eliminate the errors of this
instrument, as the possibility of such errors was constantly present in
my mind; and it is supposed that the instrumental errors did not
amount to more than one or two one-hundredths of a millimeter on the
mercury column. The proof of this will be shown in the results
obtained.

T7ie Barometer

This was of the form designed by Eortin, and was made by James
Green of New York. The tube was 3-0 cm. diameter nearly on the
outside, and about 1*7 cm. on the inside. The correction for capillarity
is therefore almost inappreciable, especially as, when it remains con-

^ These amounted to less than ‘Oiemm. at any part.

On the Mechanical Equivalent of Heat

3G3

fitant, it is exactly eliminated from the equation. The depression for
this diameter is about *08 mm., but depends upon the height of the
meniscus. The height of the meniscus was generally about 1-3 mm.;
but according as it was a rising or falling meniscus, it varied from
1-4: to 1*2 mm. These are the practical values of the variation, and
would have been greater if the barometer had not been attached to the
wall a little loosely, so as to have a slight motion when handled. Also
in use the instrument was slightly tapped before reading. The varia-
tion of the height of the meniscus from 1-2 to 1*4 mm. would affect
the reading only to the extent of -01 to -02 mm.

The only case where any correction for capillarity is needed is in
finding the temperatures of the steam at the 100® point, and will then
affect that temperature only to the extent of about 0®*005.

The scale of the instrument was very nearly standard at 0® C., and
was on brass.

At the centre of the brass tube which surrounded the barometer, a
thermometer was fixed, the bulb being surrounded by brass, and there-
fore indicating the temperature of the brass tube.

In order that it should also indicate the temperature of the barome-
ter, the w’hole tube and thermometer were wrapped in cloth until a
thickness of about 5 or G cm. was laid over the tube, a portion being
displaced to read the thermometers. This wrapping of the barometer
was very important, and only poor results were obtained before its
use; and this is seen from the fact that 1® on tlxe thermometer indi-
cates a correction of -12 mm. on the barometer, and Ixence makes a
difference of 0®-04 on the air thermometer.

As this is one of tl\e most important sources of error, I have now
devised moans of almost entirely eliminating it, and making continual
reading of the l)arometor unnecessary. This I intend doing by an
artificial atmospbere, consisting of a large vessel of air in ice, and
attached to the open tube of the manometer of the air thermometer.

The Thennoimters

The standard tlierinomoters used in my o.xpcriments arc given in
the following table on the iU‘.N;t page.

Tlie calibration of the first four tliennonieters has been described.
Tlie calibration of tlie K(*w standard was almost perfect, and no cor-
rection was thought nee(sssary. The scale divided on the tube was to
half-dogroes Fahrenheit ; but as the 32® and 212® points were not cor-
rect, it was in practice used as a thermometer with arbitrary divisions.

364

Hbnbt a. Eowlj^nd

On tttb! Meohanioal Equivalent of Heat

365

The interval between the 0® and 100® points, as Welsh found it, was
180®'12, usins' barometer at 30 inches, or 180® '05 as corrected to
760 rn-m of morcury.* At the present time it is 179® -68,* showing a
change of 1 part in 486 in twenty-five years. This fact shows that
the ordinary method of correcting for change of zero is not correct, and
that the coefScient of expansion of glass changes with time.'”

I have not been able to find any reference to the kind of glass used
in this thermometer. But in a report by Mr. Welsh we find a com-

TABLB VI.— OoBPARisoN BY Waiisn, 1852.

Mean of

Kow Standards
Nos. 4 and 14.

FastrSSSl,

Rognault.

K&w.

Troughton and
^mms

(Royal Society).

Ke-w.

82^00

82-00

88*71

88-72

+ -01

88*70

— -01

45*04

45*08

— 01

46-08

— *01

49*96

•00

49*96

*00

55*84

65*87

+ •08

65*84

•00

60*07

60*05

—02

60-06

—•01

65*89

65*41

+ •02

65*86

— 08

09-98

69*95

+ •03

69*98

• 00

74*69

*00

74*73

+ -08

80*05

80*06

+ •01

80*14

+ •09

85*80

85*88

+ •08

85*44

+ •14

90-50

90*51

+ •01

90*56

+ • 06

95*26

96-24

—02

95*40

+ •14

101*77

•00

101*94

+ *15

109*16

109*15

—•01

109*25

+ -0H

212*00

•00

213-00

*00

parison, made on March 19, 1868, of some of his thermometors with
two other thormometers,— one by PaRtre, cxamiTied and appro vou by
Regnault, and the other by Troughton and Sitntns. The thermometer
which I used was made a little more than a year after this; and it is

8 Boiling point, Welsli, Aug. 17, 1858, SIS® -17; barometer 80 in.

Freezing point, “ ** “ 8^0-05.

Boiling point, Rowland, June 22, 1878, 3120-46; barometer 760 mm.

Freezing point, “ “ ** 82o-78.

The freezing point was taken before the boiling point In either case.

0 1790*70, as determined again in January, 1879.

10 The increase shown hero is 1 In 80 nearly 1 Tt is evidently connected with the
change of zero ; for when glass has boon heated to 100®, the mean coefficient of ex-
pansion between 0 and lOOo often changes as much as 1 In 50. Hence It is not
strange that it should change 1 in 80 in twenty-live years. I believe this fact has
been noticed in the case of standards of length.

366

Henry A. Eowland

reasonable to suppose that the glass was from the same source as the
standards UTos. 4 and 14 there used. We also know that Eegnault was
consulted as to the methods, and that the apparatus for calibration
was obtained under his direction.

I reproduce the table on preceding page with some alterations, the
principal one of which is the correction of the Troughton and- Simms
thermometers, so as to read correctly at 32® and 212®, the calibration
being assumed correct, but the divisions arbitrary.

It is seen that the Kew standards and the Fastr6 agree perfectly, but
that the Troughton and Simms standard stands above the Kew ther-
mometers at 100® F.

The Geissler standard was made by Qeissler of Bonn, and its scale
was on a piece of milk glass, enclosed in a tube with the stem. The
calibration was fair, the greatest error being about 0®-015 C., at 50® 0.;
but no correction for calibration was made, as the instrument was only
used as a check for the other thermometers.

3. Results of Comparison
CalcxiUtim of Air Thermometer

This has already been described, and it only remains to discuss the
formula and constants, and the accuracy with which the different
quantities must be known.

The well-known formula for the air thermometer is

Xjr 1 -|“

l + a* J

\+hHT

1 H-l + W'

1 + a^ J

Solving with reference to T, and placing in a more convenient form,
we have

r=.

1+^^ ^ a

Y nearly,

where

and

For the first bulb.

Y = a — J = •00364.

= -0057.

= -0068.

For the second bulb,

On the Mechanioai Equivalent of Heat

367

To discuss the error of T due to errors in the constants, we must
replace a hy its experimental value, seeing that it was determined
with the same apparatus as that by which T was found. As it does
not change very much, we may write approximately

T - 100 -[1 V l¥rt V I j J '

Prom this formula we can obtain by differentiation the error in
each of the quantities, which would make an error of one-tenth of
one per cent in T. The values are for r = 40® nearly; i = 36°;
Hi^t — h== 370 mm. ; and A = 750 mm. If x is the variable,

Jx =

(lx T A i (lx

df 1000 dT‘

TABLE Vn Errors Pbodociro ah Error ih T or 1 ih 1000 at 40® C.

Hiod or h.

liM

^ constant.

constant.

bioo

Sis^oonst’nt.

constant.

Absolute

value,

•11 mm.

•27 mm.

•006

•00074

•00087

•0047

■00087

Relative

value,

Au;

0-0

•10

•13

•02

....

"x"

From this table it would seem that there should be no difidculty in
determining the 40° point on the air thermometer to at least 1 in 3000;
and experience has justified this result. The principal difficulty is in
the determination of IT, seeing that this includes errors in reading the
barometer as well as the cathetometer. For this reason, as mentioned
before, I have designed another instrument for future use, in which
the barometer is nearly dispensed with by use of an artificial atmos-
phere of constant pressure.

The value of ^does not scorn to affect the result to any great extent;

and if it was omitted altogether, the error would be only about 1 in
1000, assuming that the temperature t was the same at the detennina-
tion of the zero point, the 40° point, and the 100° point. It seldom
varied much.

The coefficient of expansion of the glass influences the result very
slightly, especially if we know the difference of the mean coefficients

3^8

Hhnbt a. Eowlajstd

between 0® and 100®, and say — 10° and + 10°. This difference I at
first determined from Eegnanlt^s tables, but afterwards made a deter-
mination of it, and have applied the correction."

The table given by Eegnault is for one specimen of glass only; and
I sought to better it by taking the expansion at 100° from the mean
of the five specimens given by Eegnault on p. 231 of the first volume
of his Relation des Experiences^ and reducing the numbers on page 237
in the same proportion. I thus found the values given in the second
column of the following table.

TABLE VIII.— ConrFioiHNT of Expa-ksion of thb Glass of the Aib Thbb-

SCOICBTBB, AOOOBDINO TO THB AlB THBBMOMBTBB.

Tempera-
ture ao-
oordlug to
Air Ther-
mometer.

Values of b
used for a first
Oaloulation.

b from
Begnault's
Table,
Glass No. 6.

Experimental Besults.

Apparent
Coemcient of
Expansion of
Mercury.

b, using
Regnauit's
Vsdue for
Mercury.i*

b, using
ReoknagePs
Value for
Mercury.!®

using
WUllner’s
Value for

Mercury.!*

30®

40®

60®

80®

100®

•0000353

•0000358

•0000356

•0000359

•0000363

•0000364

•0000368

•0000364

•0000367

•0000370

•0000378

•0000370

•00015410

•00016895

•00016891

•0000364

*0000368

•0000361

.0000364

•0000366

•0000367

•0000378

•0000276

•0000378

•00016881

•0000377

.0000377

•0000387

The second column contains the values which I have used, and one
of the last three columns contains my experimental results, the last
being probably the best. The errors by the use of the second column
compared with the last are as follows: —

y.^j-^.^from using 6ioo — = 'OQOOOOB instead of -0000011;

from using Jioo = -0000264: instead of -0000287;

or, for both together.

As the error is so small, I have not thought it worth while to entirely
recalculate the tables, but have calculated a table of corrections (see
opposite page), and have so corrected them.

u TMb was determined by means of a large weight thermometer in which the mor-
cnry had been carefully boiled. The glass was from the same tube as that of the air
thermometer, and they were cut from it within a few Inches of each other.
Kelations des EBp6riences, i, 8S8.
wpogg, Ann.^ cxiii, 135.

Experimental Physik, Wullner, i, 67.

On the Meohanioal Equivalent oe Heat 369

T= T' {1+373 (5(,. - 5„.) - (273 + 2')(y - 5)

T= T' {1 — . 000858+ (273+ T')(J>—V)\,

371 = *99975 T' approxiiuately between 0 and 40®. The last is tme
within less than ® degree. .

The two bulbs of the air thermometer used were from the same piece
of gloJH tubing, and consequently had nearly, if not quite, the same
coefficient of expansion.

In the reduction of the barometer and other mercurial columns to
zero, the coefficient *000162 was used, seeing that aU the scales were
of brass.

In •ffi.e tables the readings of the thermometers are reduced to
volumes of the tube from the tables of calibration, and they are cor-
rected for the pressure of water, which increased their reading, except
at 0®, by about 0®*01 C.

TABLE IX ^Tablb ov OoBSBorioirB.

Oorreotion.

Calculated

Temperature.

Corrected

Temperature.

9-9971

— 0029

19-9946

—0064

29-9924

, — 0076

89-9907

—0098

49-9894

— 0106

59-9865

— 0185

79*9880

— -0120

100

100-

The order of the readings was as follows in each observation: — 1st,
barometer; 2d, cathetometer; 3d, thermometers forward and backward;
4th, cathetometer; 6th, barometer, &o.,— repeating the same once or
twice at each temperature. In the later observations, two series like
the above were taken, and the water stirred between them.

The following results were obtained at various times for the value of
a with the first bulb: —

■0036604

•0036670

■0036658

*0036664

•0036676

Mean a = •00366664

870

Hbnet a. Eowland

obtained by using the coefficient of expansion of glass -0000304 at
100° or a = -0036698, using the coefficient -0000887.

The thermometers Nos. 6163, 6165, 6166, were always taken out of
the bath when the temperature of 40° was reached, except on Novem-
ber 14, when they remained in throughout the whole experiment.

The thermometer readings are reduced to volumes by the iables of
calilDration.

• 2 S 6

•206

• 3 U

•866

•280

•816

The first four series. Tables X to XIII, were made with one bulb
to the air thermometer. A new bxdb was now made, whose capacity

was 198-0 c. cm., that of the old being 801-98 c. cm. The value of
fox the new bulb was -0058. The values of h' and « were obtained as
follows;—

O > 1 '

June 8th -003G6790 753-870

June 82d -00366977 753-805

Jxme 85th -00366779 753-83 1

Mean -0036685 753-81

This value of a is calculated with the old coefficient for glass. The
new would have given -0036717.

It now remains to determine from these expcriunmls the most prob-
able values of the constants in the formula, comparing the air with
the mercurial thermometer. The formula is, as wo have found,
i=T—ai{t'-f) (&-/);
but I have generally need it in the following form:

t = a V- h - (100— /) (1 — n (100 + /) ) ,

tz= 6" V- Ho— mi (40 — <) (1 — « (40 -t- 1 )) .

TABLE XI. — Secokd Sbbibs, Novembbb 20-21, 1877.

A' = 749-67 mm.

TABLE Xin. — ^Foubth Ssbiss^ Fbbbuabt 11, 1878.

OiT THE Meobantoal EqeivaIiENt oe Hbat

378

W — 750*588 mean yalne before and after experiments.

The yalne a = *00 866 767 as obtained on the same day was need in this calcnlation.

TABL® XrV. — BiFTtt SbbIkS, Juins 8, 1878.

374

Henby a. EOWLAra

TABL£ XV. — Sixth Sxbieb, Jukb 22, 1878.

On the Mechanioaii Equivalent of Heat

376

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376

Hhnbt a. Bo'WIiAOT)

And idle foUomng relations hold among the constants:

(7 = (7' (1 + m (60 — 8400 «)) , nearly ,
a = mn,

i ^ —100®,

T=OV—t„

In these formulas t is the temperature on the air thermometer; Y is
the volume of the stem of the mercurial thermometer, as determined
from the calibration and meastired from any arbitrary point; and O',
f ,, m, and n are constants to be determined.

The best way of fnding these is by the method of least squares.
O' must be found very exactly; is only to be eliminated from the
equations; m must be found within say ten per cent, and n need only
be determined roughly. To find them only within these limits is a
very difficult matter.

Detemrination of n

As this constant needs a wide range of temperatures to produce much
effeci^ it can only be determined from thermometer No. 6167, which
was of the same glass as 6163, 6165, and 6166. It is unfortunate that
it was broken on November 21, and so we only have the experiments
of the first and second series. From these I have found n s= *003
nearly. This makes h = 233®, which is not very far from the values
found before from experiments above 100® by Eegnault on ordinary
glass.”

DetermlmUon of 0 <mi m

I shall first discuss the determination of these for thermometers
■ Nos. 6163, 6166, and 6166, as these were the principal ones used.

As No. 6163 extended from 0® to 40®, and the others only from
0® to 30®, it was thought best to determine the constants for this one
first, and then find those for 6166 and 6166 by comparison. As this
comparison is deduced from the same experiments as those from which
we determine the constants of 6163, very nearly the same result is

Some expeiimentB with Baudln thermometers at hifrh temperatures have
me about 240°, — a remarkable agreement, as the point must be uncertain to 10° or
more.

On- THB MbCHANIOAL EQUIVAIiBN-T 01 TThat 377

found as if 'we obtained the constants directly by comparison with the
air thermometer.

Hie constants of 6163 can be found either by comparison with 6167,
or by direct comparison with the air thermometer. I shall first deter-
mine the constants for ITo. 6167.

The constants 0 and for this thermometer were found directly
by observation of the 0® and 100® points; and we might assume these,
and so seek only for m. In other words, we might seek only to ex-
press the difference of the thermometers from the air thermometer
by a formula. But this is evidently incorrect, seeing that we thus
give an infinite weight to the observations at the 0® and 100® points.
The true way is obviously to form an equation for each temperature,
giving each its proper weight. Thus from the first series we find for
No. 6167,—

Weltrht. BquatlonB of Condition.

4 0 = 6-147 0 — #0,

4 17®-427 = 16-685 O' — — 930 m,

4 23® -793 — 19-167 Q — —

&o. &c.

6 100® =60-166 0 — io,

which can be solved by the method of least squares. As ## is unim-
portant, we simply eliminate it from the equations. I have thus
found, —

Wol«ht.

1 Nov. 14 O' = 1-85171 m = -000217

2 Nov. 20, 21 O' = 1-85127 m= -000172

Mean 0 = 1-86142 m = -000187

The difference in the values of m is duo to the obsei-vations not being
so good as wore afterwards obtained. However, the difference only
signifies about 0*-03 difference from the moan at the 60® point. After
November 20' the errors are seldom half of this, on account of the
greater oxperionee gained in observation.

The ratio of 0 for 6167 and C1G3 is found in the same way.

WelKht.

1 Nov. 14 -0310091

2 Nov. 20 -0309846

Mean

-0309928

378

Henry A. Howland

Hence for G163 we have in this way

G = -057381 C' = -056995 m = -000187.

By direct comparison of No. 6163 with the air thermometer, we find
the following:

Date.

Weight.

O'.

Nov. 14

•056920

•000239

Nov. 20

•056985

•000166

Jan. 25

•056986

•000226

Neb. 11

•056997

•000155

June 8

•056961

•000071

June 22

•056959

.000115

Mean -056976 ± -000004 -000154 ± -000010

The values of O' agree with each other with great exactness, and
the probable error is only ±0-°003 C. at the 40® point.

The great difEerenees in the values of m, when we estimate exactly
what they mean in degrees, also show great exactness in the experi-
ments. The mean value of m indicates a difference of only 0®-05
between the mercurial and air thermometer at the 20® point, the 0®
and 40® points coinciding. The probable error of m in degrees is only
±0®.003 C.

There is one more method of iinding m from these experiments; and
that is by comparing the values of O' with No. 6167, the glass of 6167
being supposed to be the same as that of 6163.

We have the formula

0 = 0' (l + 34-8m).

Hence

We thus obtain the following results:

Date. Weight.

Value of m.

Nov. 14

•000236

Nov. 20

•000218

Jan. 25

•000217

Feb. 11

•000197

June 8

•000215

June 22

•000216

Mean

•000213

Ox THE Mecxianioal Eqoivalext of Heat

379

The results for m are then as follows:

From direct comparison of No. 61C7 with the air thermometer •000187
From direct comparison of No. 0163 with the air thermometer *000154
From comparison of No. 01 (>3 M’ith No. (5167 -OOOSIS

The first and last are mulouhtedly the most exact numerically, but
tlicy apply to No. 6167, and are also, especially the first, derived from
somewliat higher temperatures than the 20° point, where the correc-
tion is the most important. The value of »n, as determined in cither
of these ways, depends upon the determination of a difEercncc of tem-
perature amounting to 0°-30, and hence should he quite exact.

The value of m, as obtained from the direct comparison of No. 6163
with the air thermometer, depends upon the determination of a differ-
ence of about 0°-05 between the mercurial and the air thermometer.
At the same time, the comparison is direct, the temperatures are the
same as we wish to use, and the glass is the same. I have combined
the results as follows:

«i from No. 6167 *000200

«! from No. 6163 *000154

Mean *00018“

It now remains to deduce from the tables the ratios of the constants
for the different thermometers.

The proper method of forming the equations of condition are as
follows, applying the method to the first scries:

WelBht.

4
4

where is the constant for No. 6166, (/, is that for No. 6163, and
x'o is a constant to he eliminated. Dividing by G„ the equations can

be solved for The following table gives the results :

'• Bee Appendix to Thermometry, where it ia ilnally thought beat to rejaot the
value from No. 0167 altogether.

21-26 = 115*33 — n

266-80 a,„ = 422-84 f — r,
341-06 (7„, = 634-71 6', — n
431-716',,, = 663-49 6', — f.

380

Hbnbt a. Eowiand

TABIiE XVI . — Basiob or Cohsiants.

Bate.

Weight.

6168

®6T

6166

MS?

6166

5165

6166

5I?S

6166

8!33

Nov. 14
Nov. 20
Jan. 25
Feb. 11
June 8
June 22

•081009

•080985

•040658

•040670

1-8111
1-8128
1-8122
1-8115
1-8108
1-8122
> ■

... .

8-0588

8-0605

8-0588

6-1449

6-1469

6-1438

Mean j

.080998

±.00005

.040666

±.000008

1.81175
± .0004

8.0594
± .0002

6.1451
-4" . 0004

Prom these we hare the following, as the final most probable results:

0,, = 8-0601 0„

G,„ = 1-31176 0„

0, = -031003 a, „

0„ = -24991.(7, „

(7„,= -040661 (7, „

of which the last three are only used to calculate the temperatures on
the mercurial thermometer, and hence are of little importance in the
remainder of this paper.

The value of O' which we have found for the old value of the coeffi-
cient of expansion of glass was

(7' = -056976;

and hence, corrected to the new coefficient, it is, as I have shown,

(7, =.056962.

Hence, 0„ =-46912,

(7,„ = -074720.

And we have finally the three following equations to reduce the ther-
mometers to temperatures on the air thermometer:

Thermometer Ho. 6163 :

2’=-056962 7' — i'o — -00018 r(40 — T) (1 — -003 (r-|-40)).
Thermometer Ho. 6166 :

r= -45912 7" — f/_.O0018 T (T— 40) (1 — -003 (r-f40)).
Thermometer Ho. 6166 :

r= -074720 7"' — V"—- 00018 T (T — 40) (1 — -003 (r4-40));

where 7', V, and T'" are the volumes of the tube obtained by cali-
bration; and ij'" are constants depending on the zero point, and

On the Mechanical Equivalent oe Hbat

881

of little importance where a dijBEerence of temperature is to be meas-
ured; and T is the temperature on the air thermometer.

On the mercurial thermometer, using the 0° and 100® points as fixed,
we haye the following by comparison with ITo. 6167:

Thermometer hTo. 6163; -057400 7 —

Thermometer KTo. 6165; -46266 7 — ioi

Thermometer ITo. 6166; <= -075281 7 — <o-

The Kew Standard

The Kew standard must be treated separately from the above, as the
glass is not the same. This thermometer has been treated as if its
scale was arbitrary.

In order to have variety, I have merely plotted all the results with
this thermometer, including those given in the Appendix, and d,rawn
a curve through them. Owing to the thermometer being only divided
to E., the readings could not be taken with great accuracy, and so
the results are not very accordant; but I have done the best I could,
and the result probably represents the correction to at least 0®-02 or
0®-03 at every point

W Reduction to the Absolute Scale

The correction to the air thermometer to reduce to the absolute
scale has been given by Joule and Thomson, in the Philosophical
Transactions for 1854; but as the formula there used is not correct,
I have recalculated a table from the new formula used by them in their
paper of 1862.

That equation, which originated with Rankine, can be placed in the form

PP=,0(^l — m!^D);

/i '• 1^'

where p, v, and fi are the pressure, volume, and absolute temperature
oi a given weight of the air; D is its density referred to air at 0° 0.
and 760 mm. pressure; //o is the absolute temperature of the freezing
point; and m is a constant which for air is 0®-33 0.

For the air thermometer with constant volume

r = 100 ;

Jploo po

■■■ +
or, since 2? = 1,

MV/'. = 3’- -00088

from which I have calculated the following table of corrections:

382

Henky a. Eowland

TABLE XVII. — Rbdtjotion of Aib Thbrmombtbb to Absolute Soat-b.

Air Thermometer.

fA " fifl

Absolute Temperature.

or Correction to Air
Thermometer.

0-9972

— 0028

19-9952

— 0048

39-9989

— 0061

89-9988

— 0067

49-9983

— 0068

69-9987

— 0068

69-9946

— 0064

79-9956

— 0044

89-9978

— •0023

100

100-000

200

300-087

- I - -087

800

800-093

+ -093

400

400-167

4 -167

600

600-228

4 -328

It is a curious cireumstanee^ that the point of maximum difference
occurs at about the same point as in the comparison of the mercurial
and air thermometers.

From the previous formula, and from this table of corrections, the
following tables were constructed.

TABLE XVIII Thbhmombtbr No. 616J).

Beading In
MUUmeters on
stem.

Temperatnre
on Mercurial
Thermometer,
0° and lOQo fixed.

Temperature
on Mercurial
Thermometer 0"
and40<*flxed by
Air Thermom.

Temperature
on Air Ther-
mometer.

Temperature
on Absolute
Scale from 0*’O.

Reading in
MlUlmeters on
Stem.

Temperature
on Mercurial
Thermometer,
O^andlOQo fixed.

Temperature
on Mercurial
Thermom., 0°
and 40° fixed by
Air Thermom.

o .

«.) h ,

l§

— 923

917

— •911

— oil

240

20 - 6.57

20-409

80-860

58-1

250

21-670

21.515

21-457

4 -217

4 -216

4*214

4-214

260

22-776

23-616

23-559

1-856

1-886

1-328

1-828

370

28-884

23-718

38-657

3-494

2-475

2-461

2-460

280

24-989

34-810

34-755

■ 3-681

3-604

8-584

3-688

290

26-098

25-907

2 . 5-854

100

4-767

4 - 7.38

4-707

4-706

800

37-300

37-000

26 - 9.50

6-908

5-860

5-829

5-827

810

38-811

28-108

28-060

120

7-086

6-986

6 - 9.50

6-948

830

29-435

39-314

29-169

180 .

8-170

8-111

8-071

8-069

880

80-641

30-834

80-282

140

9-804

9-237

9-193

9-190

840

81-662

81-486

81-898

150

10-486

10.. 361

10-814

10-811

860

33.782

83 -.548

83-614

160

11-668

11-485

11-483

860

38-908

. 88-000

88-080

170

13-700

13-608

13-666

12 - 6,58

870

85-028

84-778

84-748

180

13-839

13-780

13-676

13-673

880

86-148

85-884

85-804

190

14-967

14-850

14-794

14-790

890

37-261

86-994

30-979

300

16-081

15-966

15-909

15-906

400

88-877

88-108

88-094

310

17-308

17-080

17-032

17-018

410

89-492

89-210

89-306

330

230

18 - 832

19 - 440

18 - 191

19 - 301

18 - 1.33

19 - 242

18 - 137

19 - 287

430

40-004

40-814

40-816

30-345

31*453

33 - 554
33.653

34 - 750

35 - 848
3 «-« 5 ()
38-050
30 - 11)3

30 - 376

31 - 303

33-508

33 - 034

34 - 743

35 - 857

36 - 073
38-087
30-100
40 -.300

TABLE XIX. — Thbrmomhtbr No. 616.5.

BeadlDg In
Millimeters on
■ Stem.

Temperature
on Mercurial,
Thermometer,
0* and 100* fixed.

Temperature
on Mercurial
Thermom., 0*
and 40* fixed hy
Air Thermom.

Temperature
on Air Ther-
mometer.-

Temperature
on Ahsolute
Scale from 0*C.

Beading in
MlUlmeters on
Stem.

nit

iifl

Temperature
on Mercurial
Thermom., 0°
and 40° fixed by
Air Thermom.

Temperature
on Air Ther-
mometer.

Temperature
on Absolute
Scale from u° C.

— 4«4

— 460

—.457

— 4.57

280

17-!98

17-067

17-009

17-OO.S

8.5

240

18-066

17-920

17-861

17-8.57

+ •468

•f-460

+ •457

+ ■4.57

250

18-917

18-778

18-714

18-709

1-887

1*876

1-868

360

19-771

19-621

19-662

19-667

3-807

2-390

2-276

2-376

270

30-631

20-466

20-406

20-401

3-3ie

8-193

8-174

8-178

280

31-469

21-806

21-247

21-242

4-123

4-002

4-069

4-068

290

32*808

22-189

22-081

22-076

6-022

4-084

4-957

4-965

800

28-144

22-969

33-013

22-907

100

6-91B

6-872

6-841

5-889

810

23-974

28-793

28-786

38-781

110

6-804

6-758

6-714

6.713

830

34-796

24-607

24.562

24-647

120

7-685

7-638

7*590

7-688

880

35-618

25-424

25-870

26-865

180

8-664

8-600

8-459

8,456

840

26-488

26-282

26-180

26-174

140

»-48»

9.868

9*824

9-821

860

37-245

27-088

26-987

26-981

160

10-809

10-332

10-188

10-188 1

860

38-049

27-887

37-788

37-783

160

11-174

11-091

11-043

11-089

870

38-866

28-687

28-690

38-S84

170

13-088

11.947

U-896

11-898

880

29-651

29-426

29-882

29-876

180

13*900

13-803

12.749

12.746

390

80-449

80-218

80-176

80-170

190

18-760

18-665

18-601

18-698

400

81-249

81-011

80-971

80-065

200

14-619

14-508

14-458

14-450

410

82*078

81-829

81-782

81-786

310

220

16-479

16-840

16-862

16-215

16-806

16-167

16-803

16-168

430

82-801

82-611

82-677

83-681

TABLE XX. — Tubbmometbh No. 6166.

fill

jyi

131

Is*

Temperature
on Absolute
Scale from 0°O.j

;

g’ia

i||'|

|*ii

£isi

Isll

Temperature !
on Air Ther* ;
mometer. i

ij So

— 8:i6

— 886

— 834

— 584

' 280

16-378

10-386

10-§»8

16-§04

+ ■770

■h-764

+ ■769

+ -769

240

17-359

17-182

17-074

17-070

1-674

1*562

1-6.58

l-,568

250

18-043

17*908

17-849

17-846

3-868

2-860

2*886

2-885

360

18-835

18-6H6

18-627

18-622

8-166

:M88

8-115

8-114

270

U)-60»

19-464

10-405

10-400

8-941

3-HU

8-889

8-888

280

30-893

20-241

30-183

20-177

4-726

4-691

4-665

4*664

290

31-176

21-019

30-960

20-955

5-509

6-468

6-488

6-486

800

31-785

21-798

21-786

21-780

100

6-298

6-246

6-312

6-210

810

32-511

22-569

32-511

22-606

7-076

7-024

6-9Hh

6 -OHO

820

28-293

28-840

28-202

28-287

120

7-862

7-766

7*768

880

34-075

24-181

24-075

24-070

180

8-649

8-585

8-644

8-643

840

34-855

24-910

24-855

24*860

140

9-487

O'-W

9-828

9*831

850

35-684

25-687

25-684

25-628

160

10-228

10-161

10-105

10-102

860

36-415

26-466

36-413

26-406

160

11-017

10-086

10-887

10-884

870

37-441,

27-245

27-196

27-189

170

11-805

11-717

11-667

11-664

880

38*240

28-080

27-082

27-976

180

12-589

13-406

12-444

13-441

890

39-080

28-814

28*768

28-762

190

18-870

13-271

18-317

18-314

400

39-810

29-597

29-660

29-544

300

14-148

14-048

18-988

18-984

410

80-608

80-881

80*889

80*888

310

14-928

14-812

14-756

14-752

430

81-890

81-163

81*128

81-117

320

15-699

15-688

16-526

15-522

480

82-189

81-950

81-914

81-908

384

Hbnbt a. Eovl-aot)

In using these tahies a correction is of course to he made should the
zero point change.

TABLE XXI.— COBBBOTIOir of KbW StAVDABB to THB ABBOLITTIS SOAZiB.

Temperatui© 0.

OorrectLon in
decrees 0.

10®

— 08

ao*

— 05

80®

— 06

40 «

— •07

50®

—07

— 06

70®

— 04

80® 1

— 02

90®

— 01

100®

Appendix to Thexmometty

The last of January, 18'('9, Mr. S. W. Holman, of the Massachusetts
Institute of Technology, came to Baltimore to compare some -thermom-
eters -with the air thermometer; and by his kiudness I 'will giTe here
the results of the comparison which -we then made together.

As in this comparison some thennometers made by Fastrd in 1851
-were used, the results, are of the greatest interest.

The tables are calculated ■with the ne-west value fox -the coefficient of
expansion of glass. The calibration of all the thermometers, escept
the tw-o by Casella, has been examined, and found good. The Oasella
thermometers had no reservoir at the top, and could not thus be readily
calibrated after being msde. The Q-eissler also had none, but I suc-
ceeded in separating a column.

The absence of a reservoir at the top sho-uld immediately condemn
a standard, for there is no certainty in the work done with it.

Prom these tables -we would dra-w the inference that Ho. 6163 repre-
sents the air thermometer -with considerable accuracy. At the same
time, both tables would give a smaller value of m than I have used,
and not very far from the value found before hy direct comparison,
namely, -00016.

The difference from using fn= -00018 would be a little over 0° -01 0.
-at the 20“ point.

All the other thermometers stand above -the air thermometer, between
0“ and 100°, by amounts ranging between about 0“-06 and 0“-36 0.,

On the Meohanioal Equivalent oe Heat

385

TABLE XXIL— Sbtbntk Sbbibb.

Beduoed Beadlngs.

none standing belo'tr. Indeed, no table has ever been published shotr-
ing any thermometer standing ielow the air thermometer between 0®

The original readings in ice were 58 ’68 and 58 *45, to which >15 was added to
allow for the pressure of water in the comparator. This, of course, gives the same
dual result as if -15 were subtracted from each of the other temperatures. No cor-
rection was made to the others.

Probably some error of reading.

386

Hbnby a. Eowlamd

and 100®. By inference from experiments above 100® on crystal glass
by Eegnanlt, thermometers of this glass should stand below, but it
never seems to have been proved by direct experiment. The Pastr6
thermometers axe probably made of this glass, and my Bandings cer-
tainly contain lead; and yet these stand above, though on],y to a small
amonnt, in the case of the Fastr6^s.

The Geissler still seems to retain its pre-eminence as having the
greatest error of the lot.

The Baudin thermometers agree well together, but are evidently
made from another loif of glass from the ITo. 6167 used before. These
last two depart less from the air thermometer. The explanation is
plain, as Baudin had mannfactured more than one thousand ther-
mometers between the two, and so had probably used up the first stock
of glass. And even glass of the same lot differs, especially as Eegnaxilt
has shown that the method of working it before the blow-pipe affects
it very greatly.

It is very easy to test whether the calorimeter thermometers are of
the same glass as any of the others, by testiag whether they agree with
No. 6163 throTighont the whole range of 40®. The difference in the
values of m for the two kinds of glass will then be about *003 of the
difference between them at 20®, the 0® and 40® points agreeiug. The
only diBSculty is in calibrating or readiug the 100® thermometers accur-
ately enough.

The Baudin thermometers were very well calibrated, and were
graduated to tV'* so were best adapted to this kind of work.

Hence I have constructed the following tables, making the 0® and 40®
points agree.

TABLE XXiy.^CoHPABi8037 OP 6168 aku thb Bauuin Stakuarus.

6168

Mercurial

0«and40®

fixed.

7884.M

Difference.

6168

Mercurial

0»and40»

fixed.

TO16.M

Difference.

12-699

12-678

+ -026

11-609

11-684

+ -026

20-64:7

20-658

— 006

20-746

+ -016

24: -604:

24-667

82-208

82-211

— 008

29-564:

39-887

29-660

89-887

+ -014

89-858

89-868

A correction of 0®-01 was made to the zero points of these thermometers on ac-
connt of the pressure of the water.

Ok ihb Mbokanioal Eqtjitaibnt of Seat 387

Taiing the average of the two, it would seem that So. 6163 stood
about -016 higher than the meau of 7334 and 7316 at the 20° point,
or 6163 has a higher value of m by -000046 than the others.

These differ about -17 from the air thermometer at 40°, which gives
the value of m about -000104. Whence m for 6163 is -00016, as we
have found before by direct comparison with the air thermometer.

I am inclined to think that the former value, -00018, is too large,
and to take -00016, which is the value found by direct comparison, as
the true value. As the change, however, only makes at most a differ-
ence of 0°-01 at any one point, and as I have already used the previous
value in all calculations, I have not thought it worth while to go over
all my work again, but will refer to the snatter again in the final
results, and then reduce the final results to this value.

m.— OALOBIMBTEY
(a) Specific Heat of ‘Water

The first observers on the specific heat of water, such as De Luc,
completed the experiment with a view of testing the thermometer; and
it is curious to note that both De Luc and Flaugergues found the tem-
perature of ihe mixture less than the mean of the two e^ual portions
of which it was composed, and hence the specific heat of cold water
Uglm than that of warm.

The experiments of Flaugergues were apparently the best, and he
found as follows: “

8 parts of water at 0° and 1 part at 80° K. gave 19* -86 E.

2 parte of water at 0° and 2 parte at 80* E. gave 39° -81 E.

1 part of water at 0° and 8 parts at 80° E. gave 69° -87 R

But it is not at all certain that any correction was made for the
specific heat of the vessel, or whether the lose by evaporation or radia-
tion was guarded against.

The first experiments of any accuracy on this subject seem to have
been made by F. E. Neumann in 1831.“ He finds that the specific
heat of water at the boiling point is 1-0127 times that at about 28° 0.
(22° R).

The next observer seems to have been Eegnault,“ who, in. 1840,

*0Gehler, Phys. Worterbuch, 1, 641.

npogg. ulnn.. xzlii. 40.

«Ibia., II, 73.

388

Hbnet a. Eowland

found the mean specific heat between 100® 0, and 16® 0. to be 1 ’00709
and 1*00890 times that at about 14®.

But the principal experiments on the subject were published by
Eegnault in 1850,” and these have been accepted to the present time.
It is unfortunate that these experiments were all made by mixing water
above 100® with water at ordinary temperatures, it heing assumed that
water at ordinary temperatures changes little^ if any. An interpolation
formula was then found to represent the results; and it was assumed
that the same formula held at ordinary temperature, or even as low
as 0® C. It is true that Eegnault experimented on the subject at
points around 4® C. by determining the specific heat of lead in water
at various temperatures; but the results were not of sufficient accuracy
to warrant any conclusions except that the variation was not great.

Boscha has attempted to correct Eegnault^s results so as to reduce
them to the air thermometer; but Eegnault, in Oomptes Bendus, has
not accepted the correction, as the results were already reduced to the
air thermometer.

Him {Oomptes Rendus^ Ixx, 593, 831) has given the results of some
experiments on the specific heat of water at low temperatures, which
give the absurd result that the specific heat of water increases about
six or seven per cent between zero and 13® ! The method of experi-
ment was to immerse the bulb of a water thermometer in the water
of the calorimeter, until the water had contracted just so much, when
it was withdrawn. The idea of thus giving equal quantities of heat
to the water was excellent, but could not be carried into execution
without a great amount of error. Indeed, experiments so full of error
only confuse the physicist, and are worse than useless.

The experiments of Jamin and Amaury, by the heating of water by
electricity, were better in principle, and, if carried out with care, would
doubtless give good results. But no particular care seems to have
been taken to determine the variation of the resistance of the wire
with accuracy, and the measurement of the temperature is passed over
as if it T^ere a very simple, instead of an immensely difficult matter.
Their results are thus to be rejected; and, indeed, Eegnault does not
accept them, but believes there is very little change between 6® and 25®.

In Poggendorffs Annalen for 1870 a paper by Pfaundlor and Platter
appeared, giving the results of experiments around 4® 0., and deducing
the remarkable result that water from 0® to 10® C. varied as much as

*®Pogg. Ann,, Ixxlx, 241; also, Eel. d. Exp., i, 729.

Ok the Mbohakioal Equivalent op tThiat

389

twenty per cent in specific heat, and in a very irregular manner, — ^first
decreasing, then increasing, and again decreasing. But soon after an-
other paper appeared, showing that the results of the previous experi-
ments were entirely erroneous.

The new experiments, which extended up to 13° C., seemed to give
an increase of specific heat up to about 6°, after which there was appar-
ently a decrease. It is to be noted that Geissler’s thermometers were
used, which I have found to depart more than any other from the air
thermometer.

But as the range of temperature is very small, the reduction to the
air thermometer will not affect the results very much, though it will
somewhat decrease the apparent change of specific heat.

In the Journal di Physique for November, 1878, there is a notice of
some experiments of M. von Miinchausen on the specific heat of water.
The method was that of mixture in an open vessel, where evaporation
might interfere very much with the experiment. No reference is made
to the thermometer, but it seems not improbable that it was one from
Qeissler; in which case the error would be very great, as the range was
large, and reached even up to 70°0. The error of tiio Geissler would
be in the direction of making the specific heat increase more rapidly
than it should. The formula he gives for the specific heat of water at
the temperature t is

1 + -000302 1.

Assuming that the thermometer was from Geissler, the formula, re-
duced to the air thermometer, would become approximately

1 — -00009 t-f -0000016 <*.

Had the thermometer been similar to that of Eecknagel, it would
have been 1 -f- -000046 t -f- -000001 P.

It is to be noted that the first formula would actually give a decrease
of specific heat at first, and then an increase.

As all these results vary so very much from each other, we can
hardly say that wo know anything about the specific heat of water
between 0 and 100°, though Kognault’s results above that temperature
are probably very nearly correct.

It seems to me probable that my results with the mechanical equiv-
alent apparatus give the variation of the specific heat of water with
considerable accuracy; indeed, far surpassing any results which we
can obtain by the method of mixture. It is a curious result of those
experiments, that at low temperatures, or up to about 30° 0., the spe-

390

HsinaT A. ’Rowlant)

cific heat of water is about constant on the mercurial thermometer made
by Bandin, but decreases to a minimum at about 30® when the red/uction
is made to the air thermometer or the absolute scale^ or, indeed, the Kew
standard.

As this ctuions and interesting result depends upon the accurate
comparison of the mercurial with the air thermometer, I have spent
the greater part of a year in the study of the comparison, but have not
been able to find any error, and am now thoroughly convinced of the
truth of this decrease of the specific heat. But to make certain, I have
instituted the following independent series of investigations on the
specific heat of water, using, however, the same thermometers.

The apparatus is shown in Pig. 4. A copper vessel, A, about 80 cm,
in diameter and 83 cm. high, rests upon a tripod. In its interior is a
three-way stopcock, communicating with the small interior vessel B,
the vessel A, and the vulcanite spout 0, By turning it, the vessel B
could be filled with water, and its temperature measured by the ther-
mometer Z), after which it could be delivered through the Spout into
the calorimeter. As the vessel J5, the stopcock, and most of the spout,
were within the vessel A, and thus surrounded by water, and as the
vulcanite tube was very thin, the water could be delivered into the
calorimeter without appreciable change of temperature. The proof of
this will follow later.

The calorimeter, E, was of very thin copper, nickel-plated very
thinly. A hole in the back at F allowed the delivery spout to enter,
and two openings on top admitted the thermometers. A wire attached
to a stirrer also passed through the top. The calorimeter had a capac-
ity of about three litres, and weighed complete about 388-3 grammes.
Its calorific capacity was estimated at 35-4 grammes. It rested on
three vulcanite pieces, to prevent conduction to the jacket. Around
the calorimeter on all sides was a water-jacket, nickel-plated on its
interior, to make the radiation perfectly definite.

The calorific capacity of the thermometers, including the immersed
stem and the mercury of the bulb, was estimated as follows : 14 cm. of
stem weighed about 3-8 gr., and had a capacity of *8 gr.; 10 gr. of
mercury had a capacity of -3 gr.; total, 1-1 gr.

Often the vessel B was removed, and the water allowed to flow
directly into the calorimeter.

The following is the process followed during one experiment at low
temperatures. The vessel A was filled with clean broken ice, the open-
ing into the stopcock being covered with fine gauze to prevent any

On THE MEOKANIOiL EiJTnTAIiBira OE TThiat

391

small particles of ice from flowing out. The w'hole -vras then covered
with cloth, to prevent melting. The vessel -was then jBHed with water,
and the two thermometers immersed to get the zero points. The
calorimeter being about two-thirds filled with water, and having been
weighed, was then put in position, the holes corked up, and one ther-
mometer placed in it, the other being in the melting ice. An obser-
vation of its temperature was then taken every minute, it being fre-
quently stirred.

When enough observations had been obtained in this way, the cork
was taken out of the aperture F and the spout inserted, and the water
allowed to run for a given time, or until the calorimeter was full. It
was then removed, the cork replaced, and the second thermometer
removed from the ice to the calorimeter. Observations were then
taken as before, and the vessel again weighed.

Two thermometers were used in the way specified, so that one might
approach the final temperature from above and the other from below.
But no regular difference was ever observed, and so some experiments

392

Hbnbt a. Eowljlnd

were made with both thermometers in the calorimeter duriag the whole
experiment.

The priacipal sources of error are as follows:

1st. Thermometers lag behmd their true reading. This was not
noticed, and would probably be greater in thermometers with yery fine
stems like Geissler’s. At any rate, it was almost eliminated in the
' experiment by using two thermometers.

2d. The water may be changed in temperature in passing through
the spout. This was eliminated hy allowing the water to run some
time before it went into the calorimeter. The spout being yery thin,
and made of vulcanite, covered on the outside with cloth, it is not
thought that there was any appreciable error. It will be discussed
more at length below, and an experiment given to prove this.

3d. The top of the calorimeter not being in contact with the water,
its temperature may be uncertain. To eliminate this, the calorimeter
was often at the temperature of the air to commence with. Also the
water was sometimes violently agitated just before taking the final
reading, previous to letting in the cold water. Even if the tempera-
ture of this part was taken as that of the air, the error would scarcely
ever be of sufficient importance to vitiate the conclusions.

4th. The specific heat of copper changes with the temperature.
ITnimportant.

5th. Some Water might remain in the spout whose temperature might
be different from the rest. This was guarded against.

6th. Evaporation. Impossible, as the calorimeter was closed.

7th. The introduction of cold water may cause dew to be deposited on
the calorimeter. The experiments were rejected where this occurred.

The corrections for the protruding thermometer stem, for radiation,
&c., were made as usual, the radiation being estimated by a series of
observations before and after the experiment, as is usual in determin-
ing the specific heat of solids.

Jume 14, 1878, — First Experiment

Time.

Iher. ei68.

Ther. eifl*. 0 Points.

296-76

6163, 57-9

Air, 21“ 0.

296-7

6165, 34-8

Jacket about 25® 0.

296-7

6166, 20-5

296-65

OiT THE Meohanioal Eqtjitalbnt oe Hbat 393

Xlme. Iher. 6168. Tber. 6166. 0 Points.

44}-44} Water running.

Calorimeter before

3043*0

46i 318'7 351*7

“ after

3853-3

47J 318-8 851*8

Water at 0° added

810*3

48J 318-9 353-0

Thermometer

1*1

Total at 0“

811-4

Temperature before 296*6

Calorimeter before

3043-0

• Correction for 0 + *3

Weight of Vessel

388*8

396*8=36°-597

Water

1664*7

Correction for stem + *019

Capacity of calorimeter

35*4

Initial temperature of

“ thermometer

1*1

calorimeter 86®*616

Total capacity

1691*3

318*6 -f *3 = 318-8 = 17°-994

251*6 - 1 = 261-6 = 17°*962

Correction for stem —*006

Correction for stem —

*006

l7°-988

17°

*966

Mean temperature of mixture, 17° -973.

Mean specific heat 0° — 18°

_ 1691*3 X8°-644_,. 0025

- 811-4 X 17«-073 - ^

Mean specific heat 18° — 37°

Jme 14.—S«>oni Experiment

Calorimeter before 2016'3; temperature 361-4: by IKTo. 6163.
Calorimeter after 3047-0; temperature 344-5 and 388-7.

Air, 31° C.; jacket about 37°.

361-4 4- — 361-6 = 33° -803, 33°-8G3 when corrected for stem.

344-5 -3 = 344-7 = 30° -865; no correction for stem.

388-7 — 1 = 888-6 = 30° -846; no correction for stem.

Moan, 30° -855.

Mean specific heat between 0° and 31° _ j^.o()02
Mean specific' heat between ’31° and 34°

June X4.—^Mrd Experiment

Calorimeter before 1961-8; temperature 393-6 by No. 6166.
Calorimeter after 3044-6; temperature 343-7 and 313-0.

Air and jacket, about 18° C.

894

Hbjtbt a. EawiiAND

393*6 — *1 = 393*6 = 29®*036, or 29®*077 -when corrected for stem.
243*7 — 1 = 243*6 = 17° *349; no correction for stem.

213*0 + *2 = 213*2 = 17°*374; no correction for stem.

Mean, 17° *361.

Mean speoifio heat between 0° and 17° _ ^ .

Meas specific heat between 17° and 29°

It is to be observed that thermometer Uo. 6166 in all cases gave
temperatures about 0°*02 or 0°*03 below ITo. 6163. This difference
is undoubtedly in the determination of the zero points, as on June 16
the zero points were found to be 20*4 and 68*0. As one has gone up
and the other down, the mean of ike temperatures needs no correction.

Jwie IS

Calorimeter before 2068*2; temperature 364*6 by No. 6166.
Calorimeter after 2929*2; temperature 249*7 and 217*7.

Air and jacket at about 22° C.

264*6 = 26°*766, or 26°*782 when corrected for stem.

249*7 = 17° *822, or 17° *812 when corrected for stem.

217*7 + *1 = 217*8 = 17° *884, or 17°*874 when corrected for stem.

Rejected on account of great difference in finfll temperatures by the
two thermometers, which was probably due to some error in reading,

/•una

Calorimeter before 2002*7; temperature 330*3 by No. 6163.
Calorimeter after 3075*2; temperature 221*9 and 266*6.

Air and jacket, 21° C.

330*3 “j- *1 = 330*4= 30°*321, or 30°*369 when corrected for stem.

221*9 “|- *1 = 222*0 = 18° *349, or 18°*343 when corrected for stem.

256*6 -|- *0 = 266*6 = 18°*368, or 18°*352 when corrected for stem.

Mean, 18° *347.

Specific heat between 0° and 18°

BpecifSc heat between IS’’ and 30°

Jime 21

Calorimeter before 2073*8; temperature 347*8 by No. 6166.
Calorimeter after 2986*8; temperature 234*5 and 206*6.

Air and jacket, about 21° C.

On thb Meohanioaii Equitalbnt ob Hbat

39&

34'J'-8 + '0 = 347-8 = 26® •457, or 26°-471 Tten corrected for stem.

234-5 + •0 = 234-6 = 16® -648, or 16®-636 when corrected for stem.

206-6 + -1 = 206-7 = 16® -661, or 16®-644 when corrected for stem.

Mean, 16® -640.

Specific heat between 0® and 17° qqqwi

Specific heat between 17° and 25^

Rejected because dew was formed on the calo-rimeter.

A series was now tried with both thermometers in the calorimeter
from the beginning.

JiHM 2i5

Calor. before 2220-3; temperat. 326-6 by Uo. 6166; 309-9 by No. 6165.
Oalor. after 3031-4; temperat. 233-4 by No. 6166; 224-6 by No. 6165.

Air, 24®-2 C.; jacket, 23®-6.

326-6 + •0 = 326-6 = 23° -726, or 23°-726 when corrected for stem.

309-9 + -2 = 310-1 = 23°-739, or 23®-740 when corrected for stem.

g33.4_|- •0 = 233-4 = 16® -668, or 16°-546 when corrected for stem.

234.0.4. -2 = 224-8 = 16° -662, 16°-649 when corrected for stem.

Means, 23® -733 and 16® -647.

Specific heat between 0° and 1 h° _ 1.0010
Specific heat between Ifi"® and 24*’

Jvm &S

Oalor. before 2278-6; temperat. 340-35 by No. 6166; 324-1 by No. 6165.
. Oalor. after 3130-2; temperat. 242-6 by No. 6166; 232-8 by No. 6166.

Air, 23® -6 0.; jacket, 22® -6.

340-36 + -0 = 340-36 = 24® -877, or 24® -881 when corrected for stem.

324-1 + -2 = 324-3 =24® -899, or 24® -903 when corrected for stem.

242-6 +-0 = 242-6 = 17® -264, or 17® -263 when corrected for stem.

232-8 + -2 = 233-0 =17°-261, or 17®-250 when corrected for stem.

Specific heat between 0° and 17° _ , .aqom
S pecific heat between 17* and 26°

Oalor. before 2316-36; temperat. 386-1 by No. 6166; 368-4 by No. 6166.
Oalor. after 2966-90; temperat. 296-4 by No. 6166; 281-7 by No. 6166.

Air, 23° -6 0.; jacket, 22® -6.

396

HbNBT a. EoWLiJSTD

386-1 + *0 = 386-1 = 28°-466, or 28®-465 when corrected for stem.

268-4 + -2 = 368-6 = 28° -472, or 28°-482 when corrected for stem.

295-4 + -0 = 296-4 = 21° -374, or 21°-368 when corrected for stem.

281-7 + -2 = 281-9 = 21°-400, or 21°-394 when corrected for stem.

Means, 28° -473 and 21° -381.

Specific heat between 0° and 21° __ . -

Specific heat between 21° and 28° ■“

Two experiments were made on June 23 with warm water in vessel
A, readmgs being taken of the temperature of the water, as it filowed
out, by one thermometer, which was then transferred to the calorimeter
as before.

Jwf^e 28

Water in A while running, 314-16 by No. 6163.

Calor. before 1630-9; temperat. 281-1 by No. 6166.

Calor. after 2996-3; temperat. 328-4 by No. 6166; 272-7 by No. 6163.

314-15 4“ ‘1 = 314-25 = 28° -526, or 28°-562 when corrected for stem.
281-1 + -0 = 281-1 =20°-262, or 20°-268 when corrected for stem.
328-4 + -0 = 328-4 =23°-946, or 23°-960 when corrected for stem.
272-7 + -1 = 272-8 =23°-960, or 23°-966 when corrected for stem.

Specific heat between 20° and 24° _

Specific heat between 24° and 29° ”

Jvm 23

Water in A while running, 383-9 by No. 6163.

Calor. before 1624-9; temperat. 286-76 by 6166.

Calor. after 3048-2; temperat. 392-45 by 6166, and 318-1 by 6163.

383-9 -|- -1 = 384-0 =36°-303, or 36°-367 when ’corrected for stem.
286-75+ -0 = 286-75 = 20°-702, or 20°-700 when corrected for stem-
392-46 + -0 = 392-45 = 28° -954, or 28°-980 when corrected for stem.
318-1 + -1 = 318-2 =28°-964, or 28°-992 when corrected for stem.

Specific heat between 21° and 29° _ .qq- .

Specific heat between 29° and 36°

To test the apparatus, and also to check the estimated specific heat
of the calorimeter, the water was almost entirely poured out of the
calorimeter, and warm water placed in the vessel A, which was then
allowed to flow into the calorimeter.

Ok thb Mbohakioal E^trivALEKT op Bkai

397

Water in A while ruimmg, 309-0 by No. 6163.

Calor. before 391-3; temperat. 314-6 by 6166.

Calor. after 3139-0; temperat. 308-3 by 6166, and 378-5 by 6163.

Air about 81® C.

Therefore, water lost 0°-078, and calorimeter gained 6°. Hence the
capacity of the calorimeter is 39.

Ano^er experiment, more carefully made, in which the range was
greater, gare 36.

The close agreement of these with the estimated amount is, of
course, only accidental, for tliey depend upon an estimation of only
0®-08 and 0®-18 respectively. But they at least show that the water is
delivered into the calorimeter without much change of temperature.

A few experiments were made as follows between ordinary tempera-
tures and 100®, seeing that this has already been determined by Eeg-
nault.

Two thermometers were placed in the calorimeter, the temperature
of which was about 6® below that of the atmosphere. The vessel J5
was then filled, and the water let into the calorimeter, by which the
temperature was nearly brought to that of the atmosphere; the opera-
tion was then immccliately repeated, by which the ternperatAire rose
about 6° above the atmosphere. The temperature of the boiling water
was given by a thermometer whose 100® was taken several times.

As only the rise of temperature is needed, the zero points of the
thermometers in the calorimeter are unnecessary, except to know that
they are within 0®-08 of correct.

June 18

Temperature of boiling water, 99®-9.

Calor. before 8684-7; temperat. 869-8 by 6166, and 848-3 by 6166.
Calor. after 8993-8; temperat. 381-0 by 6166, and 363-4 by 6166.

269-8 = 18®-668, or 18° -666 when corrected for stem.

848-3 = 18° -664, or 18° -561 when corrected for stem.

381-0 = 88° -064, or 88° -066 when corrected for stem.

363-4 = 88° -066, or 88° -066 when corrected for stem.

Specific heat 88° — 100®
Specific heat 18® — 88°

= 1-0084.

Other experiments gave 1-0016 and 1-0060, the mean of all of which

398

Hbnbt a. Bowiand

is 1*0033. Begnault^s foTmtila gives 1*006; but going directly to bis
e:q)erimeuts, we get about 1*004, the other quantity being for 110®.

The agreement is very satisfaetoiy, though one would expect my
small apparatus to lose more of the heat of the boning water than
Eegnault^s. Indeed, for high temperatures my apparatus is much
inferior to Eegnaulfs, and sc I have not attempted any further experi-
ments at high- temperatures.

My only object was to confirm by this method the results deduced
from the experiments on the mechanical equivalent; and this I have
done, for the experiments nearly all show that the specific heat of water
decreases to about 30®, after which it increases. But the mechanical
equivalent experiments give by far the most accurate solution of the
problem; and, indeed, give it with an accuracy hitherto unattempted in
experiments of this nature.

But whether water increases or decreases in specific heat from 0® to
30® depends upon the determination of the reduction to the air ther-
mometer. According to the mercurial thermometers Nos. 6163, 6166 and
6166, treating them only as mercurial thermometers, the specific heat of
water up to 30° is nearly constant, hut by the air thermometer, or by the
Kew standard or Fastri, it decreases.

Pull and complete tables of comparison are published, and from them
any one can satisfy himself of the facts in the case.

I am myself satisfied that I have obtained a very near approximation
to absolute temperatures, and accept them as the standard. And by
this standard the specific heat of water undoubtedly decreases from 0®
to about 30®.

To show that I have not arrived at this result rashly, I may mention
that I fought against a conclusion so much at variance with my precon-
ceived notions, but was forced at last to accept it, after studying it for
more than a year, and making frequent comparisons of theomometers,
and examinations of all other sources of error.

However remarkable this fact may be, being the first instance of the
decrease of the specific heat with rise of temperature, it is no more
remarkable than the contraction of water to 4°. Indeed, in both cases
the water hardly seems to have recovered from freezing. The specific
heat of melting ice is infinite. Why is it necessary that the specific
heat should instantly fall, and then recover as the temperature rises ?
Is it not more natural to suppose that it continues to fall even after the
ice is melted, and then to rise again as the specific heat approaches infin-

On the Meohanioal Eq^hvaxent of Heat

399

ity at the toiling point? And of all the bodies ■which we should select as
probably exhibiting this property, water is certainly the first

(&.) Heat Capacity of Calorimetex

During the construction of the calorimeter, pieces of all the material
were saved in order to obtain the specific heat. The calorimeter which
Joule used was put together with screws, and with little or no solder.
But in my calorimeter it was necessary to use solder, as it was of a much
more complicated pattern. The total capacity of the solder used was
only about the total capacity including the water; and if we

should neglect the whole, and call it copper, the error would be only
about x^W* Hence it was considered sufficient to weigh the solder
before and after use, being careful to weigh the scraps. The error in
the weight of solder could not possibly have been as great as ten per
cent, which, would affect the capacity only 1 part in 18,000.

To determine the nickel used in plating, the calorimeter was weighed
before and after plating; but it weighed less after than before, owing
to the polishing of the copper. But I estimated the amount from the
thickness of a loose portion of the plating. I thus found the approxi-
mate weight of nickel, but as it was so small, I counted it as copper.
The following are the constituents of the calorimeter: —

Thick sheet copper

Thin sheet copper

Oast brass

26-1 per cent.

46-7 "

ir-9 «

* EoUed or dra^ brass

5-7

Solder

4-0

Steel

1-6

100-0

Nickel

-3

To de'bermine the mean specific heat, the basket of a Begnaultis
apparatus was filled with the scraps in the above proportion, allowing
the basket of brass gauze, which was very light, to coxmt toward the
drawn brass. The specific heat was then determined be'tween 20® and
100®, and between about 10® and 40®.' Between 20® and 100® the
ordinary steam apparatus was used, but between 10® and 40® a special
apparatus filled with water was used, the water being around the tube
containing the basket, in the same manner as the steam is in the

400

Henbt a. Eowland

original apparatns. In the calorimeter a stirrer was used, so that the
basket and water should rapidly attain the same temperature. The water
was weighed before and after the experiment, to allow for evaporation.
A co-rrection of about 1 part in 1000 was made, on account of the heat
lost by the basket in passing from the apparatus to the calorimeter, in
the 100® series, but no correction was made in the other series. The
thermometers in the calorimeter were IToe. 6163 and 6166 in the dif-
ferent experiments.

The principal diflBculty in the determination is in the correction for
radiation, and for the heat which still remains in the basket after some
time. After the basket has descended into the water, it commences to
give out heat to the water; this, in turn, radiates heat; and, the tempera-
ture we measure is dependent upon both these quantities.

Let T = temperature of the basket at the time t

{(

r =

<e it tc

{{

u a it

e =

« << water

a it a

e" =

a a a

(9"= P'.

We may then put approximately

r- y" = (r-

where c is a constant. But

fjjf _ rpn _ T' — T,

hence

To find c we have

= ((?" - (?')(! -

— ( 9 '

where 5" can be estimated sufficiently accurately to find C7' approxi-
mately.

These formula apply when there is no radiation. When radiation
takes place, we may write, therefore, when t is not too small,

- 19' = ((9" - ^)(1 - - (7 (# - io) ,

where (7 is a coefficient of radiation, and is a quantity which must be
subtracted from t, as the temperature of the calorimeter does not rise

On the Mechanical Equivalent oe Heat

401

instantaneously. To estimate T, being the temperature of the air,
ve have, according to Newton’s law of cooling,

G(t — <«) = ~~ nearly,

Afr at

U = c nearly,

where it is to be noted that - is nearly a constant for all values of

(t''— T, according to Newton’s law of cooling.

The temperature reaches a maximum nearly at the time

and if 6^ is the maximum temperature, we have the value of ff' as
follows:

and this is the final temperature provided there was no lose of heat.

When the final temperature of the water is nearly equal to that of
the air, 0 will be small, but the time <„ of reaching the maximum
will be great. If n is a constant, we can put 0 = a {0" — T,), and
0(,in + e — < 9 ) will be a minimum, when

0 =

, or T, = 0" —

0 " — 0 '
ao

That is, the temperature of the air must be lower than the tempera-
ture of the water, so that T, = ff' as nearly as possible; but the for-
mula shows that this method makes the corrections greater than if we
make T, = O', the reason being that the maximum temperature is not
reached until after an infinite time. It vrill in practice, however, be
found best to moke the temperature of the water at the beginning
about that of the air. It is by far the best and easiest method to
make all the corrections graphically, and I have constructed the follow-
ing graphical method from the formulse.

First make a series of measurements of the temperature of the water
of the calorimeter, before and after the basket is dipped, together with
the times. Then plot them on a piece of paper as in Fig. 6 , making
the scale sufficiently large to insure accuracy. Five or ten centimeters
to a degree are sufficient.

nahed is the plot of the temperature of the water of the calori-
26

402

Hbnkt a. Bowland

nieter^ the time being indicated by the horizontal line. Continue the
line d c it meets the line I a. Draw a horizontal line through
the point 1. At any point, 6, of the curve, draw a tangent and also a
vertical line t the distance e g will be nearly the value of the con-
stant c in the f ormulsB. Lay oflE 2 f equal to c, and draw the line fJiJc
through the point A, which indicates the temperature of the atmos-
phere or of the vessel surrounding the calorimeter. Draw a vertical
line, j i, through the point Tc. Prom the point of maximum, c, draw
a line, j c, parallel to d w, and where it meets Jc j will be the required
point, and will give the value of Hence, the rise of temperature,
corrected for aU errors, will be 1c j.

This method, of course, only applies to cases where the final tem-
perature of the calorimeter is greater than that of the air^ otherwise
there will be no maximum.

In practice, the line d m is not straight, but becomes more and more
nearly parallel to the base line. This is partly due to the constant
decrease of the difiEerence of temperature between the calorimeter and
the air, but is too great for that to account for it. I have traced it to
the thin metal jacket surrounding the calorimeter, and I must condemn,
in the strongest possible manner, all such arrangemients of calorimotc^rs
as have such a thin metal jacket around them. The jacket is of an
uncertain temperature, between that of the calorimeter and the air.
When the calorimeter changes in temperature, the jacket follows it but
only after some time; hence, the heat lost in radiation is uncertain.
The true method is to have a water jacket of constant temperature, and
then the rate of decrease of temperature will be nearly constant for a
long time.

The following results have been obtained by Mr. Jacques, Fellow of
the University, though the 'first was obtained by myself. Corrections
were, of course, made for the amount of thermometer stem in the air.

0% TUB Km IM' UKAr 403

Mviin Hin't'ini'

24" to loo'

■imiri

20' to !««»"

mnr*

tfft' to JiHi'

■OHOli

i;r to ao"

■oisor*

14 t** ar*’

*(1883

S» to H”

(«U0

Tn t«i thi’ in^^nn t^'iiinr-nimn* »f O' to 40", I Iwivo uw*<l

th« fttli* of iiHT**##*? fotiiwl Ity for I'ojijH’r. 'I’hoy Iht*!) b«i;nni»% for
Hu* «»’«« from o" to -lo",- -

«t«07

«o»r

tn»rn

0H1I3

09m

Mohii <wo 3 i (mnn

A* tlw* oBjwrity of Uio owlorlmotor it* whoot four jMtr «’i*nt of that of
thff total rapat'ity. incluilitijt Itio wntor, thi» pmlmltlo ornir i« about
of th« total ranarily, an«I may thitfi lo* romtitlonxl i»a aatiafa*?tory.

I liarw al«»o tlio tio'on t»|ii*fiUt* boat a* f«U«»w», from otbor

olwarw#!-”

I iimt l«l> iH'nrh .

OO'IO {tuilintt.

it03A Kt'mianit.

■O0.V.* Hi'ttnault.

otina ibbio.

003(1 Ko|*|».

0040

Thit!* riHlii«‘««l to lw‘t«*'*'H (•* aii*l ■K*"' l*y lti'‘tlo'M formula nivi** '0{t93.
Iloitro wi' bovo lb«' followiorr fttf tb** oaloritiiolor: ”

fttUM Itrti'i* ikA« nfttmiitiiiri) t«« Hawip lh)» ttAfiiit TM» HMtdfir was

I"' ?♦*> Iff 0^}ttNl itAfl* *»f lift titi4 )wl

404

Henet a. Eowland

Per cent. Speoiflo Heat between 0® and 40® C.

Copper

91-4

•0922

Zinc

•7

•0896

Tin

3-6

•0550

Lead

2-7 ,

•0310

Steel

1-6

•1110

Mean -0895

The close agreemeat of this number with the experimental result
can only be accidental, as the reduction to the air thermometer would
decrease it somewhat, and so make it even lower than mine. However,
the difference conld not at most amount to more than 0*5 per cent,
which is very satisfactory.

The total capacity of the calorimeter is reckoned as follows: —

Weight of calorimeter 3 •8712 kilogrammes.

Weight of screws *0016 kilogrammes.

Weight of part of suspending wires. . -0052 kilogrammes.

Total weight 3-8780 kilogrammes.

Capacity = 3- 878 X '0892 = -3459 kilogrammes.

To this must be added the capacity of the thermometer bulb and
several inches of the stem, and of a tube used as a safety valve, and we
must subtract the capacity of a part of the shaft which was joined to
the shaft turning the paddles. Hence,

•3459
+ -0011
+ -0010
— -0010

Capacity = -3470

As this is only about four per cent of the total cnjiacity, it is not
necessary to consider the variation of this quantity with the tempera-
ture through the range from 0® to 40® which I liave used.

IV.— DETERMniTATION' OT’ EQUIVALENT
(a.) Historical Bemarks

The history of the determination of the mechanical equivalent of heat
is that of thermod 3 mamics, and as such it is impossible to give it at
length here.

On the Mechanical Equivalent oe Heat 405

I shall simply refer to the few experiments ■which a priori seem to
possess the greatest value, and which have been made rather for the
determination of the quantity than for the illustration of a method,
and shall criticise them to the best of my ability, to find, if possible, the
cause of the great discrepancies.

1. General Beview oe Kethods

Whenever heat and mechanical energy are converted the one into
the other, we are able by measuring the amounts of each to obtain the
ratio. Every equation of thermodynamics proper is an equation
between mechanical energy and heat, and so should be able to give ■us
the mechanical equivalent. Besides this, wo axe able ■to measure a
certain amoimt of electrical energy in both mechanical and heat unite,
and thus to also get the ratio. Chemical energy can be measured in
heat units, and can also be made to produce an electric cuxrmit of known
mechanical energy. Indeed, we may sum up as follows the different
kinds of energy whose conversion into one another may furnish us wi^th
the mechanical equivalent of hea^t. And the problem in general would
be the ratio by which each kind of energy may be converted into each of
the others, or into mechanical or absolute units.

а. Mechanical energy.

б. Heat.

c. Electrical energy.

d. Magnetic energy.

6. Gravitation energy.

f. Radiant energy.

g. Chemical energy.

Capillary energy.

Of these different kinds of energy, only the first five can be measured
other than by their conversion into other forms of energy, although Sir
William Thomson, by the introduction of such terms as “ cubic mile of
sunlight,” has made some progress in the case of radiation. Hence for
these five only can the ratio be known.

Mechanical energy is measured by the force multiplied by the dis-
tance through which the force acts, and also by the mass of a body multi-
plied by half the square of its velocity. Heat is usually referred to the
quantity required to raise a certain amount of water so many degrees,
though hitherto the temperature of the water and the reduction to the
air thermometer have been almost neglected.

406

Hbitbt a. Rowland

The euergy of electricity at rest is the quantiiy nnaltiplied by half the
potemtialj or of a ciirrent, it is the atren^h of curreDt multiplied by the
electro-motive force, and by the time; or for all attractive forces varying
inversdy as the square of the distance. Sir William Thomson has given
the expression

wtere B is the resultant force at any point in space, and the integral is
taken thronghont space.

These last three kinds of energy are already measured in absolute
measure and hence their ratios are accurately known. The only ratio,
then, that remains is that of heat to one of the others, and this must be
determined by experiment alone.

But although we cannot measure f, g, Tim general, yet we can often
measure ofE equal amounts of energy of these kinds. Thus, although we
cannot predict what quantities of heat are produced when two atoms of
diflEerent substances unite, yet, when the same quantities of the same
substances unite to produce the same compoimd, we are safe in assuming
that the same quantity of chemical energy comes into play.

According to these principles, I have divided the methods into direct
and indirect.

Direct methods are those where 6 is converted directly or indirectly
into a, c, d, or e, or vice versa.

Indirect methods are those where some kind of energy, as jr, is con-
verted into 6, and also into a, c, d, or e.

In this classification I have made the arrangement with respect to
the kinds of energy which are measured, and not to the intermediate
steps. Thus Joule^s method with the magneto-electric machine would
be classed as mechanical energy into heat, although it is first converted
into electrical energy. The table does not pretend to be complete, but
gives, as it were, a bird^s-eye view of the subject. It could be extended
by including more complicated transformations; and, indeed, the sym-
metrical form in which it is placed suggests many other transformations.
As it stands, however, it includes all methods so far used, besides many
more.

In the table of indirect methods, the kind of energy mentioned first is
to be eliminated from the result by measuring it both in terms of heat
and one of the other kinds of energy, whose value is known in absolute
or mechanical units.

Indirect. A. Direct.

On the Mechanical Equtvai/Bnt of Heat 407

It is to "be noted that, although it is theoretically possible to measure
magnetic energy in absolute units, yet it cannot be done practically with
any great accuracy, and is thus useless in the determination of the
equivalent. It could be thus left out from the direct methods without
harm, as also out of the next to last teinn in the indirect methods.

TABLE XXV. — Stnofsis or Mbthods roa Obtaining thb
MbOHAIUOAL EQmVALBNT OB HbAT.

Heohanloal Energy
Gravitation

1. BeverslDle prooeea

a. Irreversible pro-
cess

a. Expansion or oompreaslon ac-
cording to adlabatlo curve.

5. Expansion or compression ac-
cording to isothermal curve.

0 . Expansion or compression ac-
cording to any curve with re-
generator.

d. Electro-magnetic engine driven
by thermo-eleotrlo pile In a
circuit of no resistance,
a. Friction, percussion, etc.
h. Heat from magneto-electric cur-
rents, or electric machine.

A Heat, Electric Energy.

1. p«««. j t

( ably).

( a. HeaUng of wire by current, or
a. Irreversible pro- { heat produced by discharge

cess ( of electric battery.

r 1, Beverslble process

y. Heat, Magnetic Energy

<u Badlant Energy, Heat

(Badlant energy absorbed
by blackened surface.)

p, Ohemlcal Energy, Heat.
(Oombustlon, etc.)

y. Capillary energy. Heat

(Heat produced when a liq-
uid is absorbed by a po-
rous solid.)

8 .

«.

Eleotnoal energy. Heat

(Heat generated In a wire
by an electrical current.)

M^etlc Energy, Heat

(Heat generated on demag-
netising a magnet.)

{

3. Irrevercdble pro-
cess

a. Mechanical Energy.

b. Eleotnoal «

0 . Magnetlo **
d. Oteavltatlon *•

a. Mechanical Energy

b. Eleotnoal **

0 . Magnetic ••
d. Gravitation ••

A. Mechanical Energy,
b. Eleotrlcal **

0 . Magnetic **

d. Gravitation ••

a* Mechanical Energy

b. Masnel^c **

0 . Gravitation **

a. Mechanical Energy

b. Eleotnoal

e. Gravitation **

0 . Thermo-electno current mag-
netising a magnet In a drcnlt
of no resistance.

a. Heating of magnet when de-
magnetised.

Orooke's radiometer.

Thermo-eleotrlo pile.

Thermo-eleotrlo pile with electro-
magnet In circuit.

1. Cannon.

3. Electro-magnet machine run by
galv. battery.

Current from battery.

Electro-magnet magnetised by a
battery current.

Movement of liquid by oapillartty.

Eleotnoal currents from oaplllair
action at surface of mercury.

Balslng of liquid by capillarity.

Magneto-electno or eleotro-mag-
netlo machine. Bleotrlo at-
traction.

Electro-magnet,

Armature attracted by a perma-
nent Magnet

Induced current on demagnetising
a magnet.

S a. Mechanical Energy, i Velocity imparted to a falling
b. Electrical t body.

0 . Magnetic **

mg body.)

408

Hbnet a. RowiiAnd

TABLE XXYl Histobioal Tablb of Ezpbbimbntal Bbbultb.

Method

G-enexal.

Method In Partlonlar.

Observer.

a Compression of air

Expansion <<

6 Theory of gases (see below).,
or vapors (see below).

c Experiments on steam-engine.

Expansion and contraction of metals. .

A a 2 a Boring of cannon

Friction of water in tubes

<< in calorimeter

** “ in calorimeter

“ “ in calorimeter

Friction of mercury in calorimeter. . . .

plates of iron

metals

(( metals in mercury calor. . .

metals

Boring of metals.

Water in balance d frottement

Flow of liquids under strong pressure.

Crushing of lead

Friction of metals

Water in calorimeter

A a 2 b Heating by magneto-electric currents. . .

Heat generated in a disc between the )
poles of a magnet y

A p 2 a Heat developed in wire of known ab- j
solute resistance 1

Do.

do.

Do.

do.

Do.

do.

Edlund'^

Rumford**

Joule“*

Joulei^

Joule'^

Joule'^*

J oule^*
Joule^*
Him^»
Favre**
Him^
Hirn^“
Him^«
Him'^
Him^u
Puluj»i»
Joule

1860-1 420-482
f 448*6
1866 J 480*1
[ 428*8

1798 940ft.lbs.
1848 424*6

1845 488*8

1847 428*9

1850 428*9

1860 424*7

1850 425*2

1857 871*6

1858 418*2

1868 400-450

1858 425*0

1860-1 482*0

1860-1 483*0

1860-1 425*0

1876 426*6

1878 428*9

Quintus
Icilius**
also Weber
Lenz, also
Weber
Joule*iH
H. F. Weber*‘^

1 1859 1

895 -4
478-9
499-5
428-16

B p a 2 Diminishing of the heat produced in a \
battery circuit when the current v

produces work )

Do. do. do.

B p b \ Heat due to electrical current, electro- '
chemical equivalent of water =
•009879, absolute resistance electro-
motive force of Danlell cell, heat "
developed by action of zinc on sul.

of copper

Heat developed in Danlell cell

Electro-motive force of Danlell cell

Weber,
Boscha,
Favre, and
Silbermann

Joule

Boscha*«

On the Mbohanioal Equivalent oe Heat 409

2. Bxsuxts oe Best Betebminations

On the basis of this table of methods I have arranged the following
table, showing the principal results so far obtained.

In giving the indirect results, many persons have only measured one
of the transformations required^ and as it would lengthen out the table
very much to give the complete calculation of the equivalent' from these
selected two by two, 1 have sometimes given tables of these parts. As
the labor of looking up and reducing these is very great, it is very
possible that there have been some omissions.

i have taken the table published by the Physical Society of Berlin,* as
the basis down to 1857, though many changes have been made even
within this limit.

I shall now take up some of the principal methods, and discuss them
somewhat in detail.

Method from Theory of Oases

As the different constants used in this method have been obtained by
many observers^ I first shall give their results,

TABLE ZXVII. — Sfeoifio Hba.t ov 0asb8.

Llniit to
Tomporaturo.

Approximate
Toxnperature
of water.

Tomperature
roduood to

SpooifloHeat.

Air ........

Mercurial

Thermometer

1 -2669 1

Delaroche and
Bdrard.

20« to 310®

26140.3 1

Air

Thermometer

^ -ssrsi"!

Begnault.

20® to 100®

so® 1

Mercurial

Thermometer

1 -SSSS"'*

E.Wiedemann.

ITydro^jen.. .

Mercurial

js-2986 1

Delaroche and
B6rard.

Thermometer

15® to 200®

13»-2

Air

Thermometer

|8-4090"‘

Begnault.

21® to 100®

21° •!

Mercurial

Thermometer

|8-410«'^>

E.Wledemann.

■■“Taking mean results on page 101 of Sel. dit Thtp., tom. li.,

410

Hbitet a. Eo-wland

TABLE XXVIU.— OoEFFioiBiTT OF ExpAKSioir OF Air triTDBR Oorstant Volume

Taking Expansion of Mercury
aooordmg to Regnault.

(Taking Expansion of Mercury
according to WuUner’s
calculation of Regnault's
Experiments.

Regnault

•0086655

•0086687

Mf^us

•0086678

•0086710

Jolly

•0086695

•0086737

Rowland

•0086675

•0086707

Mean

■0086676

•0086708

TABLE XXIX. — Ratio of Spboifio Heats of Air.

Date.

Ratio
of decide
Bt^ts.

1813

PuMlshed In

t 1-864

1819

^ 1-8748

....

1-349

. 1858

1-431

1858

i-4i9e

1859

1-4025

1861

1*8845

1863

1-41

1868

1864

1-41

1864

1869

1-803

1871 }

Results lost
in the siege

1878

of Paris.

1-4058

1874

1-397

Method.

Observer.

Method of Oldment & D^sormes, )
globe 30 litres y

Never fully published

Method of CUmentdsD^sonnes. .
Usiug Breguet thermometer. . . • ,
OUment & D^sormes, globe 89 1

Utres f

016meut & BSsormes

016ment & D^sormes, globe 10 )

litres )

Passage of gas from one vessel \
into another, globes 60 litres j
Pressure in globe changed by 1

aspirator, globe 36 litres j

Heating of gas by electric cur- )

rent y

016ment A D^sormes

Barometer under air-pump re- \
ceiver of 6 litres j

Compression and expansion of )
gas by piston y

Clement & D^sormes with metal- )
lie manometer, globe 70 litres y
Compression of gas by piston. . .

C16meut d; (

Dfisormes*^ 1

Cay-Lussac et Welter***.
Delaroche et B4rard*u
Favredt Silbermann*****.

Masson**

Welsbach***

Him****.

Oazin***^

Dupr6**^

Jamln <fc Richard**^*** . ,
Tresca et Laboulaye****
Kohlrausch**^

Regnault

Rontgen**^*

Amagat***

table XXX.— Pbikcipal Valuks of thb Velocity of Soued.

On a?Hii Mbohanical EQtnTALBNT OB Heat

411

412

Henkt a. Eowiand

Beferenees. (Tables XXVI to XXX.)

* Pbysical^Society of Berlin, Port, der Phys., 1868.

“Joule, PMl. Mag., ser. 8, toI. xxvL Bee also Mec. Wfirmefiqui valent,
Q-esammelte Abhandlungen von J. P. J oule, Braunschweig, 1873.

1“ Joule, Phil. Mag., ser. 8, vol. xxili. See also 2 above.

** ti n (( u XXVl. **

▼ tt (( (( (( xxvii.

▼1 t< H <( t( u T TVf , C4 U

Him, Th^orle M6c. de la Chaleur, ser. 1, 8“® ed.

Edlund, Pogg, Ann., cxiv. 1, 1866.

** Pavre, Comptes Bend., Peb. 16, 1868; also Phil. Mag., xv. 406.

* Violle, Ann. de China., ser. 4, xxii. 64.

Quintus Icilius, Pogg. Ann., cl. 69.

xti Boscha, Pogg. Ann., cvlli. 163.

Joule, Report of the Conamittee on Electrical Standards of the B. A., London,
1878, p. 176.

H. P. Weber, Phil. Mag., ser. 6, v. 80.

Pavre, Comptes Rend., xlvli. 699,

Regnault, Rel. des Experiences, torn. ii.
xvu E. Wiedemann, Pogg. Ann., clvli. 1.

Clement et Desormes, Journal de Physique, Ixxxix. 888, 1819.

Laplace, Mec. Celeste, v. 126.

** Masson, Ann. de Ohlm. et de Phys., ser. 8, tom. liii.

^ Welsbach, Der Civilingenieur, Neue Polge, Bd. v., 1869,

““ Him, Theorie Mec. de la Chaleur, i. 111.

Pavre et Sllbermann, Ann. de Chim., ser. 8, xxxvii. 1861.

Cazin, Ann. de Chim., ser. 8, tom. Ixvi.

Dupre, Ann. de Chim., 8“« ser., Ixvii. 869, 1808.

“"rt Kohlrausch, Pogg. Ann., cxxxvi. 618.

Rontgen, Pogg. Ann., cxlvlli. 608.

Jamin et Richard, Comptes Rend., Ixxi. 886,

Tresca et Laboulaye, Comptes Rend., Iviii. 868. Ann. du Oonserv. des Arts
et Metiers, vl. 866.

*** Amagat, Comptes Rend., Ixxvli. 1826.

Mem. de I’Acad. des Sci., 1738, p. 128.

«xii Benzenberg, Gilbert’s Annalen, xlii. 1.

Goldingham, Phil. Trans., 1838, p. 96.
xxxir Ann. de Chim., 1823, xx. 310 also, (Euvres de Arago, M6m. Sci., ii. 1.
Stampfer und Von Myrbach, Pogg. Ann., v. 496.

Moll and Van Beek, Phil. Trans., 1824, p. 424. See also Shroder van dor Kolk,
Phil. Mag., 1866.

x«vii Parry and Poster, Journal of the Third Voyage, 1834-6, Appendix, p. 86. Phil.
Trans., 1838, p. 97.

xxxvm Savart, Ann. de Chim., ser. 3, Ixxi. 30. Recalculated,
xxxix Bravais et Martins, Ann. de Chim., ser. 3, xiii. 6.

Regnault, Bel. des Exp., iii. 688.

Delaroclie et Bdrard, Ann. de Chim,, Ixxxv. 73 and 113.
xiii Pnluj, Pogg. Ann., clvii. 666.

On the Meohanioal EqtuvaiiBnt oe Heat 413

EBtimating the weight rather arbitrarily, I have combined them as
follows:

No.

4
6
6
r
8
9

Velocity at 0‘‘-O.
Dry Air.

332-6

332-7

330-9

330- 8
332-6
332-8
332-0

331- 8

332- 4
330-7

Estimated Welgrlit
of Obson-atlon.

3
7
1
1

4
10

Mean 331-76

Or, corrected for the normal carbonic acid in the atmosphere, it be-
comes 331-78 metres per second in dry pare air at 0® C.

From Eegnanlfs experiments on the velocity in pipes I find by
graphical means 331-4 m. in free air, which is very similar to the above.

OaleuUition from Properties of Gases

E— specific heat of gas at constant pressure.

Je=: specific heat of gas at constant volume.

pressure in absolute units of a unit of mass.
r= volume in absolute units of a unit of mass.
H = absolute temperature.

/= Joule’s equivalent in absolute measure.

'f'—lc'

General formula for all bodies :

414

Hhnbt a. Eowland

Also,

Application to gases; Bankine’s foimnla is, —

r» = R(,-mb.^y

If 0 , is the coefScient ol expansion hetireen 0° and 100°, then
Ma — •” (1 H“ ’OOOSStji) ,

irhence

where and are the true coefficients of expansion at the given
temperature;

According to Thomson and Joule’s experiments «i = 0'’‘33 C. for air
and about 2°-0 for COj . Hence 272” -99.

The equations should be applied to the observations directly at the
given temperature, but it will generally be sufficient to use them after
reduction to 0° 0. XTsing AT = ’SSI'S according to Eegnault for air, we
have for the latitude of Baltimore, —

Prom ESntgen’s value y = 1-4063 = 430*3.“

« Amagafs « 1*397 = 436-6.

velocity of sound 331-78m. per sec. y = 429*6.

88R6ntgen glTes the value 428-1 for the latitude of Paris as calculated by a formula
of Shroder v. d. Kolk, and 427-8 from the formula for a perfect gas, and these both
agree more nearly with my result than that calculated from my own formula.

Os THE Mechanical Equivalent oe Heat

416

TJfling Wiedemann’s valne fox E, -2389, these become

£. = 427-8 : -- = 434-0 ; — = 427-1 .

9 9 9

As Wiedemann, however, need the mercurial thermometer, and as
the reduction to the air thermometer would increase these jdgures from
•2 to -8 per cent, it is evident that Eegnaulf s value for K is the more
nearly correct. I take the weights rather arbitrarily as follows:

-Weight

ESutgeu

430-3

Amagat

436-6

Veloeily of Bound

429-6

Mean 430*7

And this is of course the value referred to water at 14® C. and in the
latitude of Baltimore. My value at this point is 427*7.

This determination of the mechanical equivalent from the properties
of air is at most very imperfect, as a very slight change in either y or
the velocity of sound will produce a great change in the mechanical
equivalent.

From Theory of Tc/pore

Another important method of calculating the mechanical equivalent
of heat is from thS equation for a body at its change of state, as for
ins'fance in vaporization. Let v be the volume of the vapor, and v the
volume of the liquid, H the heat required to vaporize a unit of mass of
the water; also let p be the pressure in absolute units, and the absolute
temperature. Then

The quantity H and the relation of p to ii have been determined with
considerable accuracy by Eegnault. To determine J it is only required
to measure the volume of saturated steam from a given weight of water;
and the principal diflBlculty of the process lies in this determination,
though the other quantities are also difficult of determination.

This volume can be calculated from the density of the vapor, but this
is generally taken in the superheated state.

416

Hbnet a. Eowland

The experiments of Fairbaim and Tate®* are probably the best direct
experiments on the density of saturated vapor, but even those do not
pretend to a greater accuracy than about 1 in 100. With Eegnaulfs
values of the other quantities, they give about Joule^s value for the
equivalent, namely 425. Him, Herwig, and others have also made the
determination, but the results do not agree very well. Herwig even
used a Geissler standard thermometer, which I have shown to depart
very much from the air thermometer.

Indeed, the experiments on this subject are so uncertain, that physi-
cists have about concluded to use this method rather for the deter-
mination of the volume of saturated vapors than for the mechanical
equivalent of heat.

From the Steam-Enffim cmd Boopamion of Metals

The experiments of Him on the steam-engine and of Edlund on the
expansion and contraction of metals, are very excellent as illustrating
the theory of the subject, but cannot have any weight as accurate deter-
minations of the equivalent.

From Friction Bisperiments

Experiments of this nature, that is, irreversible processes for con-
verting mechanical energy into heat, give by far the best methods for
the determination of the equivalent.

Eumford^s experiment of 1798 is only valuable from an historical
point of view. Joule’s results since 1843 undoubtedly give the best
data we yet have for the determination of the equivalent. The mean of
all his friction experiments of 1847 and 1850 which are given in the
table is 425-8, though he prefers the smallest number, 423-9, of 1860.
This last number is. at present accepted throughout the civilized world,
though there is at present a tendency to consider the number too small.
But this value and his recent result of 1878 have undoubtedly as much
weight as all other results put together.

As sources of error in these determinations I would suggest, first,
the use of the mercurial instead of the air thermometer. Joule com-
pared his thermometers with one made by Fastr6. In the Appendix
to Thermometry I give the comparison of two thermometers made by
Pastr6 in 1850, with the air thermometer, as well as of a large number
of others. From this it seems that all thermometers as far as measured

Phil. Mag., ser. 4, xxi, 280.

On thk Mki It hUit’ivAi.KNT iiK IIkvt

I IT

ittaitil .A(«v th.- nir thifriiimiuii-r lw;tttwn O^' mul lOO”, and that the
for ihi* Kantrw at •m" [k d"' I ('. t’ltiii); the fnrniulit ^iven
in Thtrtmmrinj thi,'* would produce an error of iilKnit .'1 in fO(Hl

Bl Jfr’O , the teiHperniure JohIi'

The M}w<i}5e h««at of copper which tlmile H«e», luimely, •(ISISIfl, it*
undoiihlrdly too large. I'jiinK the value deduced from more rw^ent
ewpcriuo’nt# in calculating the capacity of my «‘nlorimelor, ’tHlUM,
doule'a iiniidier would again he iiiercttainl lit piirta in Id.iMlO, ao that
we have,

Jouk'V value water nt 15” *70.

Reducthm to air thermomotor

tiorrcction for xiwcilic heat. »*f enp{ier. , f* 'ft
t'orrm'lioti to Uittude of Rattimorc. . . j- *5

480 «

It «h»e#i not m'lii imprithahle that Ihia ahottld Iw* atill further tn-
creaaed, that the rialuction to the air thermometer la the amalteat
adiniiMihh?. aa moat other thermoinetera which I have ftteaaured give
greater correetion, and aome even more than three tlmen aa great aa
the one here need, and would thua bring the value even lu high w* 489.

(tna Very aerhwM deftHd in Joule'a eximrimentK ia the amall range
of tempemtimr inaal, thia being only about, half a ilogree Fahrenheit,
or ahiiint ais dlvialona on hia thermometer. It would aeein almoat iin*
poaaiMn to ralihrate » Uiemiometnr ao accurately l.hat aix diviaiona
ahottld ht» aiNTiirate to one per cent, and it would eerlalnly newl a very
akillful olwener to rimd to that d«gri*e of aeeunuy. Furtitcr, the anin**
tiiermometer *' A ” waa uaed throughout the whede experiment with
water, and *** tlie «rr«*r of calihration waa hantiy idiininatml, the tem-
perature of the water heinK m*arly llin aame. In the exiHiriniont on
<)uii:kailver another thermoinefer waa uaial, and he then find* n higher
fcaolf, -181 ?, which, reiluccd a« above, givea 48“'0 nt, Baltimore.

The exjH'riwent# on the friction of iron ahould Ih> [irohaldy rejraded
on account of the large and uncertain correction for the energy given
nut in aonnd,

The recent itviwrimenia of IHTH give a value of 7T8-55, which re-
duced gju*« at Baltimore -I'ff5'8, the mhiiic na the other c.'tperimMut.

The agreement of the»e reduced valuew with my value at the aamis
temperature, tiatnely 187 .'t, U certainly very rcnmrkahle. and ahnwa
what an accurate experimenter Joule muat ho to get with hia aimplc
3T

418

Henry A. Eowland

apparatus results so near those from my elaborate apparatus, which
almost grinds out accurate results without labor except in reduction.
Indeed, the quantity is the same as I find at about 20® C.

The experiments of Him of 1860-61 seem to point to a value of the
equivalent higher than that found by Joule, but the details of the
experiment do not seem to have been published^ and they certainly
were not reduced to the air thermometer.

The method used by Violle in 1870 does not seem capable of accur-
acy, seeing that the heat lost by a disc in rapid rotation, and while
carried to the calorimeter, must have been uncertain.

The experiments of Him are of much interest from the methods
used, but can hardly have weight as accurate determinations. Some
of the methods wiQ be again referred to when I come to the description
of apparatus.

MetlhoA })y Beat Qenefruted. hy Eleotrio Owrent

The old experiments of Quintus Icilius or Lenz do not have any
except historical value, seeing that Weber’s measure of absolute resist-
ance was certainly incorrect, and we now have no means of finding its
error.

The theory of the process is as follows. The energy of electricity
being the product of the potential by the quantity, tho energy ex-
pended by forcing the quantity of electricity, Q, along a wire of re-
sistance, 12, in a second of tune, must be Q^JR, and as this must equal
the mechanical equivalent of the heat generated, we must have JII
Q^Bt, where H is the heat generated and t is the time the current Q
flows.

The principal difficulty about the determination by this method
seems to be that of finding B in absolute measure. A tabic of the
values of the ohm as obtained by different observers, was published by
me in my paper on the 'Absolute Unit of Electrical Resistance,’ in
the American Journal of Science, Vol. XV, and I give it here with
some changes.

The ratio of the Siemens unit to the ohm is now generally taken at
•9536, though previous to 1864 there seems to have been some doubt
as to the value of the Siemens unit.

Since 1863-4, when units of resistance first began to be made with
great accuracy, two determinations of the heat generated have been
made. The first by Joule with the ohm, and the second by H. P.
Weber, of Zurich, with the Siemens unit.

On the Mbohanioal EQTnvAMNT OE Heat

419

Each determination of resistance with each of these experiments
gives one value of the mechanical equivalent. As Lorenz’s result was
only in illustration, of a method, I have not included it among the exact
determinations.

TABLE XXXI.

Date.

Observer.

Value of Ohm.

Bemarks.

1849

Kirchhoff

•88 to -00

Approximately.

1851

Weber

•95 to -97

Approximately.

1862

Weber

( 1-088
(1-075

Prom Thomson’s unit.

Prom Weber’s value of Siemens unit.

1868-4

B. A. Oommittee

( 1-0000

1 -998

Mean of all results.

Corrected by Rowland to sero vel-
ocity of coil.

1870

Kohlrausch

1-0198

1878

Lorens

•975

Approximately.

1876

Bowland

-9911 M

Prom a preliminary comparison with
the B. A. unit.

1878

H. P, Weber

1-0014

Using ratio of Siemens unit to ohm,
-9586.

The result found by Joule was J = 96187 in absolute measure using
feet and degrees F., which becomes 499 '9 in degrees 0. on a mercurial
thermometer and in the latitude of Baltimore, compared with water
at 18“ -6 C.

TABLE XXXII.— EXPaBIlCBNTB Of JOVXB.

Observer.

Value of
B. A. Unit,

Keohanlcal equivalent
from Joule’^s Bxp.

Meohanioal equivalent
reduced to Air Thex^
mometer and cor-
reoted for 8p. Ht of
Copper.

B. A. Oommittee

1-0000

429-9

481-4

Ditto corrected by Rowland

-998

426-9

428-4

Kohlrausch

1-0198

488-2

489-7

Rowland

•9911

426-1

427-6

H. P. Weber

1-0014

480-5

482-0

The experiments of H. F. Weber •• gave 498-16 in the latitude of
Zurich and for 1® 0. on the air thermometer and at a temperature of
18® 0. This reduced to the latitude of Baltimore gives 498-45.

My own value at this temperature is 496-8, which agrees almost
exactly with the fourth value from my own determination of the abso-
lute unit.”

Given *9912 by mistake in the other tables.

Phil. Mag., 1878, 5th ser., v. 185.

>7 The value of the ohm found by reversing the calculation would be *992, almost
exactly my value.

4^0

Hbnet a. Eowiant>

There can be ao doubt that Joule’s result is most exact, and hence
I haye given his results twice the weight of Weber’s. Weber used a
wire of about 14 ohms’ resistance, and a small calorimeter holding only
250 grammes of water. This wire was apparently placed in the water
without any insulating coating, and yet current enough was sent
through it to heat the water 15° during the experiment. No precau-
tion seems to have been taken as to the current passing into the water,
which Joule accurately investigated. Again, the water does not seem
to have been continuously stirred, which J oule found necessary. And
further, Newton’s law of cooling does not apply to so great a range
as 16°, though the error from this sonrce was probably small. Further-

TABLE XXXIII.

SIXPBEtlICBVrS OF H. 7. WBBSR.

Mean of Joule and
Weber, arfvlnfir Joule
twice the Weight of
Weber.

Observer.

Value of
B. A. Unit.

Heohanioad equivalftnt
of Heat from Weber’s
Bxperlmexits.

Mean equivalent re-
duced to Air Ther-
mometer in the Lati-
tude of Baltimore.

B. A. Committee

1-000

427 -9

480-2

Ditto oorreeted by Rowland

• 998

424*9

437-2

EoblrauBob

1-0198

480-2

489-1

Rowland

•9911

424-1

436-4

H. F. Weber

1*0014

428-5

481-4

more, I know of no platinum which has an increase of coefficient of
•001054 for 1° 0., but it is usually given at about *003.

There can be no doubt that experiments depending on the heating
of a wire give too small a value of the equivalent, seeing that the
temperature of the wire during the heating must always be higher
than that of the water surrounding it, and hence more heat will he
generated than there should be. Hence the numbers should be slightly
mcreased. Joule used wire of plattnum-silver alloy, and Weber plati-
num wire, which may account for Weber’s finding a smaller value than
Joule, and Weber’s value would be more in error than Joule’s. Undoubt-
edly this is a serious source of error, and I am about to repeat an
experiment of this kind in which it is entirely avoided. Considering
this source of error, these experiments confirm both my value of the
ohm and of the mechanical equivalent, and unquestionably show a large
error in Kohlrausch’s absolute value of the Siemens unit or ohm.

On the Mechanical Equitaleni oe Heat 421

The experiments of Joiale and Pavre, vhere the heat generated by
a current, both when it does mechanical work and when it does not,
axe very interesting, bnt can hardly have any weight in an estimation
of the true value of the equivalent.

The method of calculating the equivalent from the chemical action
in a battery, or the electro-motive force required to decompose any
substance, such as water, is as follows:

Let JE be such dectro-motive force and e be the quantity of chemical
substance formed in battery or decomposed in voltameter per second.
Then total energy of current of energy per second is JEQ, where Q is
the current, or cQEJ, where E is the heat generated by unit of c, or
required to decompose unit of e. Hence, if the process is entirely
reversible, we must have in either case

OEJ — E.

But the process is not always reversible, seeing that it requires more
electro-motive force to decompose water than is given by a gas battery.
This is probably due to the formation at first of some unstable com-
pound like ozone. The process with a battery seems to be best, and we
can thus apply it to the Daniell cell. The following quantities are
mostly taken from Kohlrausch.

The quantity e has been found by various observers, and Kohlrausch "
gives the mean value as -009421 for water according to his units (mg.,
mm., second system). Therefore for hydrogen it is -001047.

The quantity E can be observed directly by short-circuiting the
battery, or can be found from experiments like those of Pavre and
Silbermann.

The electro-motive force E can be made to depend either upon the
absolute measure of resistance, or can be determined, as Thomson has
done, in electro-static units. In electro-magnetic unite it is

Siemens.

Ohms.

Absolute Measure
aooordfng to my
Dotormlnatlon.

After Waltenhofen

11-43

10-90

10-80x10'®

“ Kohlrausch"

11-71

11-17

11-07X10'®

After Pavre, 1 equivalent of zinc developes in the Danioll cell 28993
heat units;

. J _ E
9

•sPogg. Ann,, cxlix, 179.

Given by Kohlranscb, Pogg. Ann., cxUx, 182.

422

Hbnbt a. Eowland

On the mg., mm,, second system, we have j&i= 10-936 X lO’^S <> —
•001047, ff — 33993, ff = 9800-6 at Baltimore.

— = 444160 mm. = 444*8 metres.

Using Kohlrausch’s value for absolute resistance, he finds 466-6,
which is much more in error ilian that from my determination. I do
not give the calculation from the drove battery, because the Grove
battery is not reversible, and action takes place in it even when no
current fiows.

Thomson finds the difference of potential between the poles of a
Daniell cell in electro-static measure to be -00374 on the cm., grm.,
second system." Using the ratio 89,900,000,000 cm. per second, as I
have recently found, but not yet published, we have 111,800,000 on
the electro-magnetic system or 11-18 X 10^® on the mm., mg., second
system. This gives

— = 474.3 metres.

QmmA OriUeiam

All the results so far obtained, except those of Joule, seem to be of
the crudest descriptiouj and even when care was apparently taken in
the experiment, the method seems to be defective, or the determination
is made to rest upon the determination of some other constant whose
value is not accurately known. Again, only one or two observers have
compared their thermometers with the air thermometer, although I
have shown in ‘Thermometry’ that an error of more than one per
cent may be made by this method. The range of temperature is also
small as a general rule and the specific heat of water is assumed con-
stant.

Hence a new determination, avoiding these sources of error, seems
to be imperatively demanded.

(&.) Description of Apparatus
1. PBEa:.iumFAn.T Beuabes

As we have seen in the historical portion, the only experiments of a
high degree of accuracy to the present time are those of J oule. Looked
at from a general point of view, the principal defects of his method
were the use of the mercurial instead of the air thermometer, and the
sm^l rate at which the temperature of his calorimeter rose.

^Thomson, Papers on Electrostatics and Magnetism, p. 246.

Os’ XHB Mbokanioal Equivalent oe Heat 423

In, devising a new method a great rise of temperature in a short time
was considered to be the great point, combined, of course, with an accu-
rate measurement of the work done. For a great rise of temperature
gfreat work must he done, which necessitates the use of a steam-engine
or other motive power. For the measurement of the work done, there
is only one, principle in use at present, which is, that the work trans-
mitted by any shaft in a given time is equal to times the product of
the moment of the force by the number of revolutions of the shaft in
that time.

In mechanics it is common to measure the amount of the force
twisting the shaft by breaking it at the given point, and attaching the
two ends together by some arrangement of springs whose stretching
gives the moment. Morin’s dynamometer is an ecs:ample. Him** gives
a method which he seems to consider new, but which is immediately
recognized as Huyghens’s arrangement for winding clocks without stop-
ping them. As cords and pulleys arc used which may slip on each other,
it cannot possess much accuracy. I have devised a method by cog-
wheels which is more accurate, but which is better adapted for use in
the machine-shop than for scientific experimentation.

But the most accurate method known to engineers for measuring the
work of an engine is that of White’s friction brake, and on this I have
based my apparatus. Him was the first to use this principle in deter-
mining the mechanical equivalent of heat. In his experiment a hori-
zontal axis was turned by a steam-engine. On the axis was a pulley
with a flat surface, on which rested a piece of bronze which was to be
heated by the friction. The moment of the force with which the fric-
tion tended to turn the piece of bronze was measured, together with
the velocity of revolution. This experiment, which Him calls a lalanee
de frottemmt, was first constructed by him to test the quality of oils used
in the industrial arts. Ho experimented by passing a current of water
through the apparatus and observing the temperature of the water be-
fore and after passing through. Ho thus obtained a rough approxima-
tion to Joule’s equivalent.

He afterward constructed an apparatus consisting of two cylinders
abo'ut 30 cm. in diameter and 100 cm. long, turning one wiihin the
other, the annular space between which could be filled with water, or
through which a stream of water could be made to flow whose tempera-
ture could be measured before and after. The work was measured by
the same method as before.

^'Exposition de la Thdorie M^canlque do la CUalour, 8™« 6d., p. 18.

424

Henet a. Eowland

But in neither of these methods does Him seem to have recognized
the principle of the -work transmitted hy a shaft being equal to the
moment of the force multiplied by the angle of rotation of the shaft.
In designing his apparatus, he evidently had in view the reproduction
ia circular motion of the case of friction between two planes in linear
motion.

Since I designed my apparatus, Puluj^® has designed an instrument
to be worked by hand, and based on the principle used by Him. He
places the revolving axis vertical, and the friction part consists of two
cones mbbing together. But no new principle is involved in his appa-
ratus further than in that used by Him.

In my apparatus one of the new features has been the introduction
of the Joule calorimeter in the place of the friction cylinders of Him
or the cones of Puluj. At first sight the currents and whirlpools in
such a calorimeter might be supposed to have some effect; but when
the motion is steady, it is readily seen that the torsion of the calorimeter
is equal to that of the shaft, and hence the principle must apply.

This change, together with the other new features in the experi-
ments and apparatus, has at once made the method one of extreme
accuracy, surpassing all others very many fold.

2. GXITEEAI. BBBOBmTION

The apparatus was situated in a small building, entirely separate
from the other University buildings, and where it was free from dis-
turbances.

Pig. 6 gives a general view of the apparatus. To a movable axis, db,
a calorimeter similar to Joule^s is attached, and the whole is suspended
by a torsion wire, c. The shaft of the calorimeter comes out from the
bottom, and is attached to a shaft, a/, which receives a uniform motion
from the engine by means of the bevel wheels g and h. To the axis,
aJ, an accurate turned wheel, was attached, and the moment of
the force tending to turn the calorimeter was measured by the weights
0 and p, attached to silk tapes passing around the circumference of the
wheel in combiTia.tion with the torsion of the suspending wire. To this
axis was also attached a long arm, having two sliding weights, q and r,
by which the moment of inertia could be varied or determined.

«Pogg. Ann., civil, 487.

"Joule’s latest results were publisbed after this was written, and I was not aware
that he had made this improvement until lately. The result of his experiment, how-
ever, reached me soon after, and I have referred to it In the paper, but I did not see
the complete paper until much later.

On the Meohanioal Equitalbnt of Heat

Fig. 6.

426

Hbnbt a. Eowland

The number of reyolutions wae determined by a chronograph, which
received motion by a screw on the shaft if, and which made one revo-
lution for 103 of the shaft. On this chronograph was recorded the
transit of the mercury over the divisions of the thermometer.

Around the calorimeter a water jackei^ tu, made in halves, was
placed, so that the radiation could be estimated. A wooden box sur-
rounded the whole, to shield the observer from the calorimeter.

The action of the apparatus is in general as follows: As the inner
paddles revolve, the water strikes against the outer paddles, and so
tends to turn the calorimeter. TPhen this force is balanced by the
weights op, the whole will be in equilibrium, which is rendered stable
by the torsion of the wire cd. Should any slight change take place in
the velocity, the calorimeter will revolve in one direction or the other
until the torsion brings it into equilibrium again. The amount of tor-
sion read off oh a scale on the edge of Jel gives the correction to be
added to or subtracted from the weights op.

One observer constantly reads the circle M, and the other constantly
records the transits of the mercury over the divisions of the ther-
mometer.

A series extending over from one half to a whole hmr, and recortl-
ing a rise of 15“ 0. to perhaps 36“ C., and in which a record was made
for perhaps each tenth of a degree, would thus contain several hundred
observations, from any two of which the equivalent of heat could be
determined, though they would not all be independent. Such a series
would evidently have immense weight; and, in fact, I estimate that,
neglecting constant errors, a single series has more weight than all of
Joule’s experiments of 1849, on water, ptit together,

The correction for radiation is inversely proportional to tho ratio of
the rate of work generated to the rate at which the heat is lost;
and this for equal ranges of temperature is only ^ as groat in my
measures as in Joule’s; for Joule’s rate of increase was aboxit 0“-(J2 0,
per hour, while mine is about 36“ 0. in the same time, and can bo in-
creased to over 45® C. per hour.

8. DetaHiS
flVie OaVyrimeter

Joule’s calorimeter was made in a very simple manner, with few
paddles, and without reference to the production of currents to mix

« Forty experiments, with an average rise of temperature of C-Se F., equal to
0®'81 C., gives a total rise of IS®-* C., which Is only ahont two-thirds tho average of
one of my experiments. As my work Is measured with equal aeouracy, and my
radiation with greater, the statement seems to he correct.

Osr THE Mbohanioal EQurvALBiin; ob Heat 487

up the water. Hence the paddles were made without solder, and were
screwed together. Indeed, there was no solder about the apparatus.

But, for my purpose, the number of paddles must be multiplied, so
that there shall be no jerk in the motion, and that the resistance may
be great; they must be stronger, to resist the force frpm the engine,
and they must be light, so as not to add an uncertain quantity to the
calorific capacity. Besides this, the shape must be such as to cause
the whole of the water to run in a constant stream past the thermom-
eter, and to cause constant exchange between the water at the top and
at the bottom.

Bio. 7. Bio. 8.

Fig. 7 shows a section of the calorimeter, and Fig. 8 a perspective
view of the revolving paddles removed from the apparatus, and with the
exterior paddles removed from aroxmd it; which could not, however, be
accomplished physically without destroying them.

To the axis cb, Fig. 7, which was of steel, and 6 mm. in diameter, a
copper cylinder, ad, was attached, by moans of four stout wires at a,
and four more at f. To this cylinder four rings, g, Jt, i , ;, were attached,
which supported the paddles. Each one had eight paddles, but each
ring was displaced through a small angle with reference to the one
below it, so that no one paddle came over another. This was to make
the resistance continuous, and not periodical. The lower row of pad-
dles were turned backwards, so that they had a tendency to throw the
water outwards and make the circulation, as I shall show afterwards.

428

Henbt a. Eowland

iLround these movable paddles were the stationary paddles, consist-
ing of five rows of ten each. These were attached to the movable
paddles by bearings, at the points c and h, of the shaft, and were re-
moved with the latter when this was taken from the calorimeter.
When the whole was placed in the calorimeter, these outer paddles were
attached to it by means of four screws, Z and m, so as to be immovable.

The cover of the calorimeter was attached to a brass ring, which
was nicely groimd to another brass ring on the calorimeter, and which
could be made perfectly tight by means of a little white-lead paint.
The shaft passed through a stuffing-box at the bottom, which was
entirely within the outer surface of the calorimeter, so that the heat
generated should all go to the water. The upper end of the shaft
rested in a bearing in a piece of brass attached to the cover. In the
cover there were two openings, — one for the thermometer, and the
other for filling the calorimeter with water.

Prom the opening for the thermometer, a tube of copper, perforated
with large holes, descended nearly to the centre of the calorimeter.
The thermometer was in this sieve-like tube at only a short distance
from the centre of the calorimeter, with the revolving paddles outside
of it, and in the stream of water, which circulated as shown by the
arrows.

This circulation of water took place as follows. The lower paddles
threw the water violently outwards, while the upper paddles were pre-
vented from doing so by a cylinder surrounding the fixed paddles.
The consequence was, that the water flowed up in the space between
the outer shell and the fixed paddles, and down through the central
tube of the revolving paddles. As there was always a little air at the
top to allow for expansion, it would also aid in the same direction.
These currents, which were very violent, could be observed through
the openings.

The calorimeter was attached to a wheel, fixed to the shaft a&, by

OiT THE Mbohanioal Eqditaleitt oe Hbat 489

the method shown in Pig. 9. At the edge of the wheel, which was of
the exact diameter of the calorimeter, two screws were attached, from
which wires descended to a single screw in the edge of the calorimeter.
Through the wheel, a screw armed with a vulcanite point pressed upon
the calorimeter, and held it firmly. Three of these arrangements, at
distances of 120®, were used. To centre the calorimeter, a piece of
vulcanite at the centre was used. By this method of suspension very
little heat could escape, and the amount could be allowed for by the
radiation experiments.

The Toreion Bvstem

The torsion wire was of such strength that one millimeter on the
scale at the edge of the wheel signified 11-8 grammes, or about
the weights op generally used. There were stops on the wheel, so
that it could not move through more than a small angle. The weights
were suspended by very flexible silk tapes, 6 mm. or 8 mm. broad and
0-3 mm. thick. They varied from 4-6 k. to 8-6 k. taken together. The
shaft, ai, was of uniform size throughout, so that the wire e suspended
the whole system, and no weight rested on the bearings.

The pulleys, m, n, Pig. 6, were very exactly turned and balanced, and
the whole suspended system was so free as to vibrate for a considerable
time. However, as will be shown hereafter, its freedom is of little
consequence.

The Wetter Jacket

Around the calorimeter, a water jacket, f u, was placed, so that the
radiation should bo perfectly definite. During the preliminary experi-
ments a simple tin jacket was used, whose temperature was determined
by two thermometers, one above and the other below, inserted in tubes
attached to the jacket.

The Driving Gear

The cog-wheels, g, h, were made by Messrs. Brown and Sharpe, of
Providence, and were so well cut that the motion transmitted to the
calorimeter must have been very uniform.

The Chronograph

The cylinder of the chronograph was turned by a screw on the shaft
of, received one revolution for 102 of the paddles; 166 revolutions
of the cylinder, or 16,810 of the paddles, could be recorded, though.

430

Heney a. Eowland

when necessary, the paper could he changed without stopping, and the
experiment thus contiaued without interruption.

TTie Frame and Foimdaiion

The frame was very massive and strong, so as to prevent oscillation;
and the whole instrument weighed about 600 pounds as nearly as could
be estimated. It was placed on a solid brick pier, with a firm f ounda-
“ tion m the ground. The trembling was barely perceptible to the hand
when running the fastest.

T7ie Engine

The driving power was a petroleum engine, which was very efficient
in driving the apparatus with uniformity.

The Balance

For weighing the calorimeter, a balance capable of showing the
presence of less than ^ gramme with 16,000 grammes was used. The
weights, however, by Schickert, of Dresden, were accurate among them-
selves to at least 6 mg, for the larger weights, and in proportion for
the smaller. A more accurate balance would have been useless, as will
be seen further on.

Adjmtmmte

There are few adjustments, and they were principally made in the
construction.

In the first place, the shafts a!b and ef must be in line. Secondly,
the wheels rm must be so adjusted that their planes are vertical, and
that the tapes shall pass over them symmetrically, and that their edges
shall be in the plane of the wheel Tcl.

Deviation from these adjustments only produced small error.

(c.) Theory of the Experiment
1. EerniATioN or Woke Bone

The calorimeter is constantly receiTing heat from the friction, and
is giving out heat hy radiation and condnction. Now, at any given
instant of time, the temperature of the whole of the calorimeter is not
the same. Owing to the violent stirring, the water is undoubtedly at
a very uniform temperature throughout. But the solid parts of the
calorimeter cannot be so. The greatest difference of temperature is
evidently soon after the commencement of the operation. But after

On the Mbohaeioal Equivalent of Heat 431

some time the apparatus reaches a stationary state, in which, hut for
the radiation, the rise of temperature at all points would be the same.
This steady state will he theoretically reached only after an infinite
time; but as most of the metal is copper, and quite thin, and as the
whole capacity of the metal work is only about four per cent of the
total capacity, I have thought that one or two minutes was enough to,
allow, though, if others do not think this time sufficient, they can
readily reject the first few observations of each series. When there
is radiation, the stationary state will never he reached theoretically,
though practically there is little difference from the case where there is
no radiation.

The measurement of the work done can be computed as follows.
Let M he the moment of the force tending to turn the calorimeter, and
dO the angle moved by the shaft. The work done in the time t will
be fltdd. If the mom!ent of the force is constant, the integral is
simply MO I but it is impossible to obtain an engine which runs with
perfect steadiness, and although we may he able to calculate the inte-
gral, as far as long periods are concerned, by observation of the torsion
circle, yet we are not thus able to allow for the irregularity during one
revolution of the engine. Hence I have devised the following theory.
I have found, by experiments with the instrument, that the moment of
the force is very nearly, for high velocities at least, proportional to the
square of the velocity. For rapid changes of the velocity, this is not
exactly true, but as the paddles are very numerous in the calorimeter,
it is probably very nearly true. We have then

where (7 is a constant. Hence the work done beco-mes

As we allow for irregularities of long period by readings of the tor-
sion circle, we can assume in this inyestigation that the mean velocity
is constant, and equal to v^. The form of the variation of the velocity
must be assumed, and I shall put, without further discussion.

We then find, on integrating from o to 0,

w = + |c*).

Hbnbt a. Eowlaih)

which, is the work on the calorimeter during one revolution of the
engine.

The equation of the motion of the calorimeter, supposing it to he
nearly stationary, and neglecting the change of torsion of the suspend-
ing wire, is

where m is the moment of inertia of the calorimeter and its attach-
ments, ^ is the angular position of the calorimeter, W is the sum of
the torsion weights, and D is the diameter of the torsion wheel. Hence,

it + i<?-) - WD-\

7/1 ^

Wien = (l + ^c®), tie caloriiiiieter ■will merely oscillate
around a girea position, and will read its TnayimTiTn at tie times t = 0,

^ A, A, &C.

Tie total ampltade of ead oscillation will be very nearly

d,—df —

^ jr*TO 27t*ni

. If X is tie amplitude of ead oscillation, as measured in millimetres,
on tie edge of tie wled of diameter P, we lave <p —

Hence ^ =

wlere n is tie number of revolutions of tie engine per second.

Having found c in this way, the work vrill be, during any time.

w = 7zWDJS' {! + <?),

wlere N is tie total number of revolutions of the paddles.

A variation of tie velocity of ten per cent from tie mean, or twenty
per cent total, would tlus only cause an error of one per cent in tie
equivalent.

Hence, altlougl tie engine was only single acting, yet it ran easily,
lad great excess of power, and was very constant as far as long periods
were concerned. Tie engiue ran very fast, making from 200 to 350
revolutions per minute. Tie fly-wleel weigled about 330 pounds, and
lad a radius of feet. At four turns per second, tlis gives an energy
of about 3400 foot-pounds stored in the wheel. Tie calorimeter re-
quired about one-lalf lorse-power to drive it; and, assummg the same

On the Mechanical Equivalent of Heat 433

for the engine friction, we have about 140 foot-pounds of -work re-
quired per revolution. Taking the most unfavorable case, where all
the power is given to the engine at one point, the velocity changes
during the revolution about four per cent, or c would nearly equal .02,
causing an error of 1 part in 2500 nearly. By means of the shaking
of the calorimeter, I have estimated c as follows, the value of m being
changed by changing the weight on the inertia bar, or taking it oflE
altogether. The estimate of the shaking was made by two persona
independently.

X Observed.

c oaloulated.

2,200,000 grms. cm.*

*6 mm.

*016

8,100,000 “

*36 “

*013

11,800,000 “

•13 «

*017

Mean,

c = *015

causing a correction of 1 part in 5000.

Another method of estimating the irregularity of running is to put
on or take off weights until the calorimeter rests so firmly against the
stops that the vibration ceases. Estimated in this way, 1 have found
a little larger value of c, namely, about -017.

But as one cannot be too careful about such sources of error, I
have experimented on the equivalent with different velocities and with
very different ways of running the engine, by which c was greatly
changed, and so have satisfied myself that the correction from this
source is inappreciable in the present state of the science of heat.

Hence I shall simply put for the work

w = xJfWV,

in gravitation measure at Baltimore. To reduce to absolute measure,
we must multiply by the force of gravity given by the formula

= 9*78009 + -0608 8in>y,

which gives 9*8006 metres per second at Baltimore. If the calorimeter
moved without friction, no work would be required to cause it to
vibrate back and forth, as I have described; but when it moves with
friction, some work is required. When I designed the apparatus, I thus
had an idea that it would be best to make it as immovable as possible
by adding to its moment of inertia by means of the inertia bar and
weights. But on considering the subject further, I see that only the
excess of energy represented by ohzNWD can be used in this way. For,
when the calorimeter is rendered nearly immovable by its groat moment
28

4.34

Heney a. Rowland

of inertia, the work done on it is, as we have seen, ttNWD (1 + c®) ;
but if it had no inertia, it is evident that the work woxild be only
tcNWD, If, therefore, the calorimeter is made partially stationary,
either by its moment of inertia or by friction, the work will be some-
where between these two, and the work spent in friction will be only
so much taken from the error. Hence ia the latter experiments the
inertia bar was taken off, and then the calorimeter constantly vibrated
through about half a millimeter on the torsion scale.

Besides this quick vibration, the calorimeter is constantly moviug to
the extent of a few millimetres back and forth, according to the vary-
ing velocity of the engine. As frequent readings were taken, these
changes were eliminated^ In very rare cases the weights had to be
changed during the experiment; but this was very seldom.

The vibration and irregular motion of the calorimeter back and forth
served a very useful purpose, inasmuch as it caused the friction of the
torsion apparatus to act jSrst in one direction and then in the other, so
that it was finally eliminated. The torsion apparatus moved very
freely when the calorimeter was not in position, and would keep
vibrating for some minutes by itself, but with the calorimeter there
was necessarily some binding. But the vibration made it so free that
it would return quickly to its exact position of equilibrium when drawn
aside, and would also quickly show any small addition to the weights.
This was tried in each experiment.

To measure the heat generated, we require to know the calorific
capacity of the whole calorimeter, and the rise of temperature which
would have taken place provided no heat had been lost by radiation.
The capacity of the calorimeter alone I have discussed elsewhere, find-
ing the total amount equal to -347 k. of water at ordinary tempera-
tures. The total capacity of the calorimeter is then A -f- -347, where
A is the weight of water. Hence Joule^s equivalent in absolute meas-
ure is

r__ 102nnWD

(A + -uijit - t')

where n is the number of revolutions of the chronograph, it making
one revolution to 102 of the paddles.

The corrections needed are as follows:

1st. Correction for weighing in air. This must be made to TV, the
cast-iron weights, and to A + -347, the water and copper of the calori-
meter. If ^ is the density of the air under the given conditions, the
correction is — 835 X.

On the MbOHANIOAL EquiTALENT OE TTha'p 435

2a. For the weight of the tape by which the weights are hung.

mv • '0006

This IS — nr"*

sa. For the expansion of torsion wheel, D' being the aiameter at
20° a This is -000018 (<" — 20°). Hence,

P + ~ ^ ~ ’

where t — f is the rise of the temperature correctea for raaiation.

2. Radiation

The correction for raaiation varies, of course, with the aiflerence of
temperature between the calorimeter ana jacket^ but, owing to the
rapia generation of heat, the correction is generally small in proportion.
The temperature generated was generally about 0°-6 per minute. The
loss of temperature per minute by radiation was approximately ■ OOMtf °
per minute, where is the difference of the temperature. This is one
per cent for 10° -7, and four per cent for 14° -2. Generally, the calori-
meter was cooler than the jacket to start with, and so a rise of about
20° could be accomplished without a rate of correction at any point
of more than four per cent, and an average correction of less than two
per cent. An error of ten per cent is thus required in the estimation
of the radiation to produce an average error of 1 in 600, or 1 in 260
at a single point. The coefficients never differ from the mean more
than about two per cent. The observations on the equivalent, being
at a great variety of temperatures, check each other as to any error in
the radiation.

The losses of heat which I place under the head of radiation include
conduction and convection as well. I divide the losses of heat into the
following parts: 1st. Conduction down the shaft; 2d. Conduction by
means of the suspending wires or vulcanite points to the wheel above;
3d. True radiation; 4th. Convection by the air. To get some idea of
the relative amounts lost in this way, we can calculate the loss by
conduction from the known coefiBcients of conduction, and we can get
some idea of the relative loss from a polished surface from the experi-
ments of Mr. Hichol. In this way I suppose the total coefficient of
radiation to be made up approximately as follows:

Conduction along shaft -00011

Conduction along suspending wires -00006

True radiation -00017

Convection -00106

Total

-00140

436

Hbnet a. Eowland

The conduction through the vulcanite only amounts to •0000008-

Prom this it would seem that three-fourths of the loss is due to
radiation and convection combined.

The last two losses depend upon the difference of temperature be-
tween the calorimeter and the jacket, but the first two upon the differ-
ence between the calorimeter and frame of the machme and the wheel
respectively. The frame was almiys of very nearly the same tempera-
ture as the water jacket, but the wheel was usually slightly above it.
At first its temperature was noted by a thermometer, and the loss to
it computed separately; but it was found to be unnecessary, and finally
the whole was assumed to be a function of the temperature of the
calorimeter and of the jacket only.

At first sight it might seem that there^ was a source of error in
having a journal so near the bottom of the calorimeter, and joined to
it by a shaft. But if we consider it a moment, we shall see that the
error is inappreciable; for even if there was friction enough in the
journal to heat it as fast as the calorimeter, it would decrease the
radiation only seven per cent, or make an average error in the experi-
ment of only 1 in 700. But, in fact, the journal was very perfectly
made, and there was no strain on it to produce friction; besides which,
it was connected to a large mass of cast-iron which was attached to
the base. Hence, as a matter of fact, the journal was not appreciably
warmer after running than before, although tested by a thermometer.
The difference could not have been more than a degree or so at most.

The warming of the wheel by conduction and of the journal by fric-
tion would tend to neutralize each other, as the wheel would be warmer
and the journal cooler during the radiation experiment than the fric-
tion experiment.

The usual method of obtaining the coefficient of radiation would be
to stop the engine while the calorimeter was hot, and observe the
cooling, stirring the water occasionally when the temperature was read.
This method I used at first, reading the temperature at intervals of
about a half to a whole hour. But on thinking the matter over, it
became apparent that the coefficient found in this way would be too
small, especially at small differences of temperature; for the layer
next to the outside would be cooled lower than the mean temperature,
and the heat could only get to the outside by conduction through the
water or by convection currents.

Hence I arranged the engine so as to run the paddles very slowly,
so as to stir the water constantly, taking account of the number of

On the Mechanical Equivalent oe Heat 437

the revolutions and the torsion, so as to compute the work. As I had
foreseen, the results in this case were higher than by the other method.
At low temperatures the error of the first method was fifteen per cent;
but at high, it did not amount to more than about three to five per
cent, and probably at very high temperatures it would almost vanish.

I do not consider it necessary to give all the details of the radiation
experiments, but will merely remark that, as the calorimeter was nickel-
plated, and as seventy-five per cent of the so-called radiation is due
to convection by the air, the coefficients of radiation were found to be
very constant under similar conditions, even after long intervals of
time.

The experiments were divided into two groups; one when the tem-
perature of the jacket was about 5° 0., and the other when it averaged
about 30® C. ^

The results were then plotted, and the mean curve drawn through
them, from which the following coefficients were obtained. These
coefficients are the loss of temperature per minute, and per degree
difference of temperature.

table XXXV.*— CoBFrxciBNTB or Radiation,

Dlfferenoe be-

' **•'“■** -

tween Jacket and
Calorimeter.

Jacket 6^.

Jacket 20°.

•00188

-00184

•00185

•00180

+ 5

•00187

■00188

•00142

■00188

•00148

■00144

•00164

■00160

•00158

.00164

As the quantity of water in the calorimeter sometimes varied slightly,
the numbers should be modified to suit, they being true when the total
capacity of the calorimeter was 8-76 kil. The total surface of the
calorimeter was about 3350 sq. cm., and the unit of time one rmnuie.
To compare my results with those of McFarlane and of Nichol given
in the Proc. R, S. and Proc. R. S. B., I will reduce my results so that
they can be compared with the tables given by Professor Everett in his
^ Illustrations of the Ccntimeter-Gramme-Second System of Units, ^
pp. 50, 51.

[There is no table numbered XXXIV.J

438

Hbnbt a. Eowlan’d

The reducing factor is -0621, and hence the last results for the jacket
at 20® C. become :

TABLE XXXVI.

Dlfferenoe of
Temperature.

Ooefflolent of Radla-
tlon on the 0. 0. S.
System.

MoFarlane's

Value.

Batio.

•000081

•000168

•000082

•000178

•000086

•000186

•000089

•000198

•000098

•000201

•000096

•000207

The variation which I jBnd is almost exactly that given by McFar-
lane, as is shown by the constancy of the column of ratios. But my
coefficients are less than half those of McFarlane. This may possibly
be due to the fact that the walls of McFarlane^s enclosure were black-
ened, and to his surface being of polished copper and mine of polished
nickel; his surface may also have been better adapted by its form to
the loss of heat by convection. The results of KTichol are also much
lower than those of McFarlane.

The fact that the coefficients of radiation are less with increased
temperature of jacket is just contrary to what Dulong and Petit found
for radiation. But as I have shown that convection is the principal
factor, I am at a loss to check my result with any other observer.
Dulong and Petit make the loss from convection dependent only upon
the difference of temperature, and approximately upon the square root
of the pressure of the gas. Theoretically it would seem that the loss
should be less as the mean temperature rises, seeing that the air be-
comes less dense and its viscosity increases. Should we substitute
density for pressure in Dulong^s law, we should have the loss by con-
vection inversely as the square root of the mean absolute temperature,
or approximately the absolute temperature of the jacket. This would
give a decrease of one per cent in the radiation for about 6®, which is
not far from what I have found.

To estimate the accuracy with which the radiation has been obtained
is a very difficult matter, for the circumstances in the experiment are
not the same as when the radiation was obtained. In the first place,
although the water is stirred during the radiation, yet it is not stirred
so violently as during the experiment. Further, the wheel above the
calorimeter is warmer during radiation than during the experiment.

On the Mechanical Equiyalent of Heat

439

Both these sources of error tend to give too small coefl&cierLtB of radia-
tion, and this is conjBrmed by looking over the final tables. But I have
not felt at liberty to make any corrections based on the final results, as
that would destroy the independence of the observations. But we are
able thus to get the limits of the error produced.

During the preliminary experiments a water jacket was not used,
but only a tin case, whose temperature was noted by a thermometer
above and below. The radiation imder these circumstances was larger,
as the case was not entirely closed at the bottom, and so permitted more
circulation of air.

3. COBBEOTIOWS TO THERMOMBTEZRS, ETO.

Among the other corrections to the temperature as read off from
the thermometers, the correction for the stem at the temperature of
the air is the greatest. The ordinary formula for the correction is
•000166n(^ — r). But, in applying this correctio-n, it. is difficult to
estimate n, the number of degrees of thermometer outside the calo-
rimeter and at the temperature of the air, seeing that part of the stem
is heated by conduction. The uncertainty vanishes as the thermometer
becomes longer and longer, or rather as it is more and more sensitive.
But even then some of the uncertainty remains. I have sought to
avoid this uncertainty by placing a short tube filled with water about
the lower part of the thermometer as it comes out of the calorimeter.
The temperature of this was indicated by a thermometer, by aid of
which also the heat lost to the water by conduction through the ther-
mometer stem could be computed; this, however, was very minute com-
pared with the whole heat generated, say 1 in 10,000.

The water being very nearly at the temperature of the air, the stem
above it could be assumed to be at the temperature of the air indicated
by a thermometer hung within an inch or two of it. The correction for
stem would thus have to be divided into two parts, and calculated
separately. Calculated in this way, I suppose the correction is perfectly
certain to much less than one hundredth of a degree: the total amount
was seldom over one-tenth of a degree.

Among the uncertain errors to which the measurement of tempera-
ture is subjected, I may mention the following:

1. Pressure on bulb. A pressure of 60 cm. of water produced a
change of about 0®'01 in the thermometers. When the calorimeter
was entirely closed there was soon some pressure generated. Hence
the introduction of the safety-tube,— a tube of thin glass about 10 cm.

440

Henet a. Eowland

long, extending through a cork in the top of the calorinaeter. The top
of the safety-tube was nearly closed by a cork to prevent evaporation.
Had the tube been shorter, water would have been forced out, as well
as air.

2. Conduction along stem from outside to thermometer bulb. To
avoid this, not only was the bulb immersed, but also quite a length of
stem. As this portion of the stem, as also the bulb, was surrounded
by water in violent motion, there could have been no large error from
this source. The immersed stem to the top of the bulb was generally
about 5 cm. or more, and the stem only about -8 cm. in diameter.

3. The thermometer is never at the temperature of the water, be-
cause the latter is constantly rising; but we do not assume that it is
so in the experiment. We only assume that it lags behind the water
to the same amoimt at all parts of the experiment, and this is doubt-
less true.

To see if the amount was appreciable, I suddenly threw the apparatus
out of gear, thus stopping it. The temperature was observed to con-
tinue rising about 0®-02 0. Allowing 0°-01 for the rise duetto motion
after the word ^^Stop^^ was given, we have about 0®*01 0. as the
amount the thermometer lagged behind the water.

4. Evaporation. A possible source of error exists in the cooling of
the calorimeter by evaporation of water leaking out from it.

The water was always weighed before and after the experiment in
a balance giving ^ gramme with accuracy. The normal amount of
loss from removal of thermometer, wet corks, &c., was about 1 gramme.
The calorimeter was perfectly tight, and had no leakage at any point
in its normal state. Once or twice the screws of the stufling-box
worked loose, but these experiments were rejected.

The evaporation of 1 gramme of water requires about 600 heat ixnits,
which is sufficient to depress the temperature of the calorimeter about
0°*07 C. As the only point at which evaporation could take place was
through a hole less than 1 nun. diameter in the safety-tube, I think it
is reasonable to assume that the error from this source is inappreciable.
But to be doubly certain, I observed the time which drops of water of
known weight and area, placed on the warm calorimeter, took to dry.
From these experiments it was evident that it would require a consid-
erable area of wet surface to produce an appreciable effect. This wot
surface never existed unless the calorimeter was wot by dew deposited
on the cool surface. To guard against this error, the calorimeter was
never cooled so low that dew formed; it was carefully rubbed with a

On the Meoha-nioal EQxnvALENT OF Heat 441

towel, and placed in the apparatus half an hour to an hour before the
experiment, exposed freely to the air. The surface being polished, the
slightest deposit of dew was readily visible. The greatest care was
taken to guard against this source of error, and I think the experiment
is free from it.

(d.) Results
1. Constant Data

Joule’s equivalent in gravitation measure is of the dimensions of
length only, being the height which water would have to fall to be
heated one degree. Or let water flow downward with uniform velocity
through a capillary tube impervious to heat; assuming the viscosity
constant, the rate of variation of height with temperature will bft
Joule’s equivalent.

Hence, besides the force of gravity the only thing required in abso-
lute measure is some length. The length that enters the equation
is the diameter of the torsion wheel. This was determined under a
microscope comparator by comparison with a standard metre belong-
ing to Professor Eogers of Harvard Observatory, which had been
compared at Washington with the Coast Survey standards, as well as
by comparison with one of our own metre scales which had also been
so compared. The result was -26908 metre at 20° 0.

To this must be added the thickness of the silk tape suspending the
weights. This thickness was carefully determined by a micrometer
screw while the tape was stretched, the screw having a flat end. The
result was -00031 m.

So that, finally, D' = -26939 metre at 20° 0. Separating the con-
stant from the variable parts, the formula now becomes

f = ^ •

g = 9*8006 at Baltimore.

It is uimecessary to have the weights exact to standard, provided they
are relatively correct, or to make double weighings, provided the same
scale of the balaace is always used. For both numerator and denomi-
nator of the fraction contain a weight.

2. Experimental Data and Tables of ltS}S>ULTfi

In exhibiting the results of the experiments, it is much more satisfac-
tory to compute at once from the observations the work necessary to
raise 1 kil. of the water from the first temperature observed to each sue-

SsNBY A. Howland

ceeduig temperature. By interpolation in such, a table we can then
reduce to even degrees. To compare the different results I have then
added to each table such a quantity as to bring the result at 20® about
equal to 10,000 Mlogramme-metres.

The process for each experiment may be described as follows. The
calorimeter was first filled with distilled water a little cooler than the
atmosphere, but not so cool as to cause a deposit of dew. It was then
placed in the machine and adjusted to its position, though the outer half
of the jacket was left off for some time, so that the calorimeter should
become perfectly dry ; to aid which the calorimeter was polished with a
cloth. The thermometer and safety-tube were also inserted at this
time.

After half an hour or so, the chronograph was adjusted, the outer half
of the jacket put in place, the wooden screen fixed in position, and all
was ready to start. The engine, which had been running quietly for
some time, was now attached, and the experiment commenced. Pirst the
weights had to be adjusted so as to produce equilibrium as nearly as
possible.

The observers then took their positions. One observer constantly
recorded the transit of the mercury over the divisions of thermometer,
making other suitable marks, so that the divisions could be afterwards
recognized. He also read the thermometers giving the temperatures
of the air, the bottom of the calorimeter thermometer, and of the wheel
just above the calorimeter; and sometimes another, giving that of the
cast-iron frame of the instrument.

The other observer read the torsion wheel once every revolution of
the chronograph cylinder, recording the time by his watch. He also
recorded on the chronograph every five minutes by his watch, and like-
wise stirred the water in the jacket at intervals, and read its temper-
ature.

The recording of the time was for the purpose of giving the connect-
ing link between the readings of the torsion circle and of the ther-
mometer- This, however, as the readings were quite constant, had
only to be done roughly, say to half a minute of time, though the rec-
ords of time on the chronograph were true to about a second.

The thermometers to. read the temperature of the water in the jacket
were graduated to C., but were generally read to 0®-l 0., and had
been compared with the standards. There was no object in using more
delicate thermometers.

After the experiment had continued long enough, the engine was

On thb Mbohanioal Eqtjitaibnt ob Hbat

443

stopped and a radiation experiment begun. Tbe last operation was to
weigh the calorimeter again, after removing the thermometer and safety
tube, and also the weights which had been used.

The chronograph sheet, having then been removed from the cylin-
der, had the time records identified and marked, as well as the ther-
mometer records. Each line of the chronograph record was then ntun-
bered arbitrarily, and a table made indicating the stand of the ther-
mometer and the number of the revolutions and fractions of a revolu-
tion as recorded on the chronograph sheet. The times at whidi these
temperatures were reached was also found by interpolation, and re-
corded in another column.

Prom the column of times the readings of the torsion circle could be
identified, and so aU the necessary data would be at hand for calculating
the work required to raise the temperature of one kilogramme of the
water from the first recorded temperature to any succeeding tempera-
ture.

As these temperatures usually contained fractions, the amount of
work necessary to raise one kilogramme of the water to the even degrees
could then be found from this table by interpolation. Joule’s equiva-
lent at any point would then be merely the difference of any two suc-
ceeding numbers; or, better, one tenth the difference of two numbers
situated 10° apart, or, in general, the difference of the numbers divided
by the difference of the temperatures.

It would be a perfectly simple matter to make the record of the tor-
sion circle entirely automatic, and I think I shall modify the apparatus
in that manner in the future.

It would take too much space to give the details of each experiment;
but, to show the process of calculation, I will give the experiment of
Doc. I?, 1878, as a specimen. The chronograph sheet, of course, I
cannot give. The computation is at first in gravitation measure, but
afterwards reduced to absolute measure.

The calorimeter before the experiment weighed 12-2788 kil.

The calorimeter after the experiment weighed 12-2716 kil.

Mean T2-2720kil.

Weight of calorimeter alone 3-8721 Ml.

. •. Water alone weighed 8-3999 kil.

-3470 Ml.

8-7469 Ml.

Total capacily

444

Henbt a. Howland

The correction for weighing in air was -835^= -00106.

The total term containing the correction is therefore -99878.

log 86-324 =1-9361316

log -99878 = 1-9994698

1-9356014
log 8-7469 = -9418542

log const, factor = -9937472 = log 9-85706.

Hence the work per kilogramme is 9-85706 2'lfn in gravitation
measure^ the term 2'Wn being nsed to denote the sum of products
similar to Wn as obtained by simultaneous readings of torsion circle
and records on chronograph sheet.

Zero of torsion wheel, 79-3 mm.

Value of 1 mm. on torsion wheel -0118 kil.

The following were the records of time on the chronograph sheet: —

Time observed. Bevolutions of Ohronograpb. Time oaloulated.

15 8-74 15-2

20 25-32 20-1

26 42-10 26-0

30 69-06 30-0

36 76-00 36-0

40 93-03 40-0

46 109-97 46-0

60 126-92 60-0

66 144.14 66-0

The times were calculated by the formula

Time = -294 X Eevolutions -f- 12-66,

which assumes that the engine moves with uniform velocity. As the
principal error in using an incorrect interpolation formula comes from
the calculation of the radiation, and as this formula is correct within
a few seconds for all the higher temperatures, we can use it in the cal-
culation of the times.

The records of the transits of the mercury over the divisions of the
thermometer were nearly always made for each division, but it is use-
less to calculate for each. I usually select the even centimeters, and
take the mean of the records for several divisions on each side.

While the mercury was rising 1 cm. on No. 6163, there would be

On the Meohanioal Eqtjiyalent op Heat

445

about seven revolutions of the chronograph, and consequently seven
readings of the torsion circle, each one of which was the average for a
little time as estimated by the eye.

I have obtained more than thirty series of results, but have thus far
reduced only fourteen, five of which are preliminary, or were made with
the simple jacket instead of the water jacket, the radiation to which
was much greater, as there was a hole at the bottom which allowed more
circulation of the air. The mean of the preliminary results agrees so
closely with the mean of the final results, that I have in the end given
them equal weight.

On March 24th, the same thermometer was used for a second experi-
ment directly after the first, seeing that the chronograph failed to work
in the first experiment until 8° was reached. The error from this cause
was small, as the first experiment only reached to 26® C., and hence
there could have been no change of zero, as this is very nearly the tem-
perature at which the thermometer was generally kept.

Having thus calculated the work in conjunction with the tempera-
ture, I have next interpolated so as to obtain the work at the even de-
grees. The tables so formed I have combined in two ways : first, I have
added to the column of work in each table an arbitrary number, such as
to make the work at 20® about 10,000, and have then combined them as
seen in Table LI, and, secondly, I have subtracted each number from
the one 10® farther down the table, and divided the numbers so found
by 10, thus obtaining the mechanical equivalent of heat.

In these tables four thermometers have been used, and yet they were
so accurate that little difference can be observed in the experiments
which can be traced to an error of the thermometer, although the Kew
standard has some local irregularities. The greatest difference between
any column of Table LI and the general mean is only 10 kilogramme-
metres, or 0-023 degree, and this includes all errors of calibration of
thermometers, radiation, &c. This seems to me to be a very remarkable
result, and demonstrates the surpassing accuracy of the method. In-
deed, the limit of accuracy in thermometry is the only limit which we
can at present give to this method of experiment. Hence the large
])roi)ortional time spent on that subject.

The accuracy of the radiation is demonstrated, to some extent, by
the agreement of the results obtained oven with different temperatures
of the jacket. But on close observation it seems apparent that the
coefficients of radiation should bo further increased as there is a ten-
dency of the end figures in each series to become too high. This is

446

HmmT A. Eowland

exactly •what we should suppoee, as we have seen that nearly all sources
of error tend in the direction of making the radiation too small. For
instance, an error came from not stirring the water during the radiation,
and there must he a small residual error from not stirring so fast
during radiation as during the experiment. Besides this, some parts
around the calorimeter were warm during the radiation which were cool
during the experiment. And both of iihese make the correction for
radiation too small. However, the error from this source is small, and
cannot possibly affect the general conclusions. In each column of
Tables LI and LII a dash is placed at the temperature of the jacket,
and for fifteen degrees below this point the error in the radiation must
produce only an inappreciable error in the equivalent: taking the ob-
servations within this limit as the standards, and rejecting the others,
we should still arrive at very nearly the same conclusions as if we ac-
cepted the whole.

Most of the experiments are made with a weight of about Y-S kil., as
everything seemed to work best with this weight But for the sake
of a test I have run the weight up to 8-6 and down to 4-4 kil., by which
the rate of generation of the heat was changed nearly three times.
By this the correction for the radiation and the error due to the irregu-
larity of the engine are changed, and yet scarcely an appreciable differ-
ence in the results can be observed.

The tables explain themselves very well, but some remarks may be
in order. Tables XXX VII to L inclusive are the results of fourteen
experiments selected from the total of about thirty, the others not hav-
ing been worked up yet, though I propose to do so at my leisure.

Table LI gives '&e collected results. At the top of each column the
date 'of the experiment and number of the thermometer are given, to-
gether with the approximate torsion weight and the rate of rise of tem-
perature per hour. The dash in each column gives approximately the
temperature of the jacket, and hence of the air. There are four col-
umns of mean values, but the last, produced from the combination of
the table by parts, is the best.

Table LII gives the mechanical equivalent of heat as deduced from
intervals of 10“ on Table 11. The selection of intervals of 10“ tends
to screen the variation of the specific heat of water from view, but a
smaEer interval gives too many local irregularities. In taking the
mean I have given all the observations equal weight, but as the Kew
standard was only graduated to F. it was impossible to calibrate it
so accurately as to avoid irregularities of 0“-02C. which would affect

On the Mbohanioal Equivalent op Heat Wi

the quantities 1 in 600. Hence, in drawing a curve through the results,
as given in the last column, I have almost neglected the Kew, and have
otherwise sought to draw a regular curve without points of inflection.
The figures in the last column I consider the best.

Table LIII takes the mean values as found in Tables LI and LII,
and exhibits them with respect to the temperatures on the different
thermometers, to the different parts of the earth, and also gives the
reduation to the absolute scale. I am inclined to favor the absolute
scale, using m= *00016, as given in the Appendix to Thermometry,
rather than *00018, as used throughout the paper.

Table LIT gives what T consider the find result of the experiment.
It is based on the result m= *00016 for the thermometers,* and is cor-
rected for the irregularity of the engine by adding 1 in 4000.

The minor irregularities are also corrected so that the results signify
a smooth curve, without irregularity or points of contrary flexure.
But the curve for the work does not differ more than three kilogramme-
metres from the actual experiment at any point, and generally coincides
with it to about one kilogramme-metre. These differences signify
0®*007 C. and 0®*002 C., respectively. The mechanical equivalent is
for single degrees rather than for ten degrees, as in the other tables.

TABLE XXXVII.— PxBsr Sbrxbb.—

January 16, 1878. Jacket and Air about l^*’ 0.

Oorreotlon.

S.|s

Stem .

Bad .

140

52-0

— 006

9? 185

5-485

(9. KAO

160

66-0

—•008

— 017

11-412

18-028

1 -ouv

051

848

5728

180

59*2

—•022

18-650

80-652

1 -flbio
7. ililO

1006

776

6155

208

68*4

+ •006

— 015

16-280

45-820

7. QAit

8010

1202

6582

220

66 -S

+ •011

— 001

18-187

66-241

8825

1629

7000

240

70*2

+ •020

+ •027

20-802

69-168

f • ooa

ff.KtKA

4786

2056

7486

252

74*0

+ •028

+ •067

22-588

81-484

7 . QUO

6702

2484

7864

280

80*0

+ •045

+ •161

25-948

101-214

7156

2912

8292

- ^ -

8840

8720

. ! . .

8767

0147

....

4108

9578

....

4619

9999

5048

10428

5472

10852

5809

11279

6826

11706

. . * «

6758

12188

—

7180

12560

448

Hbitet a. Rowland

TABLE XXXVIII. — Bbookd Sbbibs. — Jhreliminary.

March 7, 1878. Jacket 18®.6 to 22o.6. Air about 21® C.

1 .
ii

Oorrection.

•+»

M ss

S d

Time.

M ip

« a ,

stem

sgs

170

19-9

-•016

18° 687

5-08

7-787

7-710

7.666

7-642

7-641

7.680

7.611

7.600

7.696

7.682

7.652

7.547

7.676

7-611

7-604

7-611

7-617

7-602

7-692

7-676

7-560

7-660

®18

198

7010

180

18-646

11-12

474

625

7487

190

14-756

17 •32

947

1052

7864

200

15-868

28-86

1421

1480

8292

210

26*8

-•010

-.086

16-972

29-55

1897

1909

8721

220

■ • • •

18-086

85-70

2869

2888

8146

280

* . * *

19-196

41-90

284S

2761

9578

240

20-805

48-09

8819

8189

10001

250

88.8

+ .008

-•086

21-419

64-80

8794

8615

10427

260

* * > •

22-688

4041

10858

270

> * ft *

28-642

66-69

4740

4467

11279

280

....

24-754

72-92

5218

4892

11704

290

40-8

+ 0-20

— 001

26-867

79-16

6687

5818

12180

800

• • ft ft

26-990

85-42

6164

5744

12556

810

. * . •

28-119

91-67

6648

6168

12980

820

• ■ . •

29-258

97-98

7125

6598

18405

880

47*8

+ •044

•f -078

80-898

104-28

7608

7017

18829

840

850

860

51*4

81- 640

82- 689
88-842

110-67

117-12

128-54

8097

8590

9081

7441

7867

8294

14258

14679

15106

870

55-6

+ •072

+ •184

84-998

180-04

9576

8722

15584

880

ft « • «

86-158

186-56

10071

9149

15961

890

58-7

+ •588

+ •261

87-821

148-08

10667

9677

16889

10004

10480

16816

...

—

17242

TABLE XXXIX — Third Sbbibs.— JVcKmCwary.
March 12, 1878. Jacket 18®-2 to 16®-6. Air about 15® C.

Thermometer
No. 8166.

Time.

Correction.

Corrected

Temperature.

§P

^ IS
J||

P 009

Temperature.

M S

Work per
Kilogramme
+ 7699.

stem.

Bad.

205

28-0

14-868

8-156

210

28-6

4 -002

14-7.54

6-884

164

'soii

7808

220

29-9

15-529

9-770

^7-0107

495

696

8295

280

81-1

+ •008

+ •010

16-807

14-184

827

|l7

1122

8721

In the calculation of this column, more esract data were used than giyen in the
other two columns, seeing that the original calculation was made every 5 mm. of the
thermometer. Hence the last figure may not always agree with the rest of the data.

46 As this table was originally calculated for every 5 mm. on the thermometer, I
have given the weights which were used to check the more exact calculation.

On thb Mbohanioai. Equivalent op Heat

+ -009

+ •021

+ •014

+ •088

+ •019

+ 065

+ •024

+ •089

+ •080

+ •120

+ •088

+ •159

+ ■047

+ •202

+ •056

+ •261

+ •066

+ •804

17-090

17- 875

18- 06a

19- 45S
90-242
21-029

21- 825

22- 619
28-418

24- 220

25- 028
28-825

26- 628

27- 488

28- 258

29- 069

29-884

80- 708

81 - 519

18-642

28-080

27-550

82-014

86-474

40-924

45-424

49-888

54-802

58-844

68-866

67.874

72-408

76-987

81-560

86-100

90-720

95-816

99-920

TABLE XL.— POUKTH SBRiHS.—iVtf Ziminary. «
March 24, 1878. Jacket 5®-4 to 8° -2. Air about 6® 0.

S'*

|§

0 8-071 42-864

9-204 48-898

+ •019 10-840 55-488

11-480 62-066

+ -050 12-620 68-669

18-763 75-880

+ -098 14-908 81-978

16-064 88-697

+ •150 17-202 95-264

18-860 101-941

+ •222 19-504 108-588

+ -078 +*899 24-124 185-158

26-288 141-808

+ -084 +-524 26-456 148-427

The first part of the experlmeuts was lost, as the pen of the chronograph did
not work.

450

Hbnbt a. Eowland

TABLE XLI.— Eifth Sbbibs.— JYsKfninaFp.

March 24, 1878. Jacket 5‘‘-4 to 8®-4. Air ahont 6»C.

TABLE ELII — Sixth Bbbibs.

May 14, 1878. Jacket 12®*1 to IB'’^. Air about 18® C.

Thermometer

On the Mechanical Equitaleni oe Heat

TABIilS XLII.——

7*1446

8806

8676

7*1686

• • • «

• ■ ■ •

7*1280

4778

6148

7*1844

5614

6878

7*1802

6240

6600

7*1117

6962

452

Henet a. EowiiAisrD

TABLE XLIII.—

ill

Time.

Oorreotion.

H Pi

■84

60 id

2^*

-1

M II

®|-

800

58.6

81. §66

88.71

) 7.2504

6697

7028

12125

810

55.0

+ .082

+ .127

22.665

88.42

6087

7454

12551

820

66.4

28.471

98.14

7.2898

6879

7888

13980

880

67.8

+ .089

+ .172

24.281

97.88

6722

8807

13404

840

59.2

26.088

102.61

) 7.8047

7065

8729

18830

850

60.5

+ .046

+ .222

25.896

107.86

7410

9157

14364

860

61.9

26.706

112.14

[7.8889

7769

9582

14679

870

68.2

+ .056

+ .279

27.528

116.88

8104

10009

IS 106

880

64.6

28.846

121.62

[7.4109

8454

890

66.0

+ .066

29.172

126.84

8801

400

67.4

29.996

181.12

[7.4866

9165

410

68.8

+ .076

+ .419

80.837

186.90

3 7.4581

9508

420

70.1

+ .080

+ .456

81.668

140.66

9861

TABLE XLIT ^Eighth Sbeiba.

May 38, 1878. Jacket 16°.3 to 16®.5. Air about 20® 0.

Thermometer i

No. 6166.

Time.

Oorreotion.

(Borneo ted
Temperature.

380

28.9

— .007

16?387

89.120

A QlQfy

• « • «

240

25.4

17.068

48.983

D. VlDf

888

806

8715

250

26.8

1 6.9858

- r —

785

9144

260

2^8

1168

9572

270

29.7

.000

+ .005

19.406

58.603

1888

1592

lOOOl

380

81.2

30.190

68.608

D. VUU (

1678

2019

10438

290

82.7

30.978

68.428

6.9125

2010

2446

10855

800

84.2

21.765

78.851

6.8878

2846

2871

11380

810

85.6

+ .008

+ .040

22.564

78,288

6.8866

2682

8298

11707

820

87.1

28.860

88.345 !

6.8504

8020

8722

12181

380

88.6

9 m m 9

99mm

24.161

88.814

6.8858

8868

4150

13559

840

40.1

+ .017

+ .086

24.952

98.294

6.8748

8703

4574

13988

860

41.6

....

• 9 mm

26.761

98.375

6.0184

4044

4909

18408

860

48.1

....

m 9 m 9

26.562

108.382

6.0444

4885

5428

18882

870

44.6

+ .028

+ .144

27.861

108.216

6.9201

4727 !

5851

14260

880

46.0

■ « • •

9 9 • 9

28.176

118.269

6.9888

5074

6275

14684

890

47.5

• • • •

9999

28.989

118.281

6.9885

5418

■ • • .

- • . •

400

49.0

+ .089

+ .217

29.80G

1 128.829

6.0444

5766

1 , ,

• • * .

410

50.6

. . . .

9999

80.634

c 128.899

6.9467

6115

. ,

* B •

420

62.1

+ .047

+ .281

81.446

; 188.480

6.9814

6464

....

OlT THB MBOHANIOAL EQUIVALENT OE HbAT

453

TABLE ELY.— Nisth SBRias.

May 37, 1878. Jacket 19<>.8 to 30«. Air about 38° 0.

Bevolutlons of
Chronograph

M n

Temperature.

ifi

200

— 016

15.°890

6.88

‘

8298

210

89.4

17.000

11.74

\ 8.8108

478

8719

220

40.9

-.oil

liWil

18.106

17.17

946

901

9147

280

42.8

19.219

22.62

\8.7841

1419

1826

9672

240

48.8

— oil

20.829

38.18

1895

1764

10000

260

46.8

21.442

88.68

o.oOoO

2868

2180

10426

260

....

+ .002

-.004

22.652

* « » *

2606

10852

270

....

f o . 4o00

m m m m

8081

11277

280

49.8

+ .6i2

50.56

8785

8467

11708

290

51.8

56.26

1 8.4899

4268

8888

12129

300

52.9

+ .019

+ .087

27.006

61.98

4787

4812

12668

810

54.4

67.68

1 8.4765

5215

4784

12980

320

+ .029

+ .072

29.264

78,86

5697

5169

18405

380

57.5

80.404

79.16

1 8.4562

6182

5584

18880

840

59.1

+ .043

+ .118

81.652

84.97

6669

6010

14266

360

60.6

82.702

90.86

1 8.4015

7169

6485

14681

360

62.2

+ .066

+ .178

88.868

96.78

7662

6860

15106

870

68.8

85.011

102.66

t 8.4222

8148

7286

15582

880

66.4

+ .071

+ .242

80.170

108.59

8688

7714

15960

390

EiO

87.881

114.46

1 8.4706

9128

8188

16884

400

68.6

+ .088

+ .822

88.497

120.86

9626

8566

16811

410

70.3

80.664

126.88

) 8.4816

10126

8988

17284

420

71.8

+ .106

+ .419

40.888

182.26

10620

9414

17660

9842

18088

10268

18614

...

....

10691

18987

464

HbNET a. EoWIiAiTD

TABLE XL VI Tenth Series.

June 3, 1878. Jacket 18°.l to 18®.4. Air about 20® 0.

Tbermometer
No. 6166.

Time.

Oorrectlon.

Correoted

Temperature.

5 o

'^1

Mean ‘Weight W,

^11

Temperature.

Stem.

260

4.1

-.007

17.888

7.83

9145

260

7.0

18.617

14.3899

....

496

9673

270

9.9

-.OOS

+ .004

19.401

28.19

667

925

10001

280

12,8

20.188

80.95

U.8919

1005

1860

10426

290

16.7

+ .008

+ .020

20.978

88.70

1841

1778

10854

300

18.7

21.768

46.41

U.3912

1676

2204

11380

310

21,6

+ .008

+ 0.087

22.551

54.21

2014

2637

11708

820

24.5

28.854

62.04

U.3907

2854

8054

12180

380

27.6

+ .014

+ .078

24.162

69.92

2696

8479

12555

340

80.5

24.970

77.92

U.8624

3041

8004

13980

350

88.6

+ .030

+ .182

36.780

85.89

3885

4882

18408

360

36.6

26.593

98.94

U.8542

8781

4852

18828

870

89.6

+ .028

+ .198

37.416

102.06

IHHIi

4081

6179

14255

380

42.7

28.246

110.84

U.8863

4487

6604

14680

890

45.8

+ .086

+ .281

29.079

118.49

4786

....

400

48.9

29.911

126.06

U.8078

6141

....

410

63.0

+ .877

80.764

184.89

5499

. .

TABLE XLVII.— Eleventh Series.

June 19, 1878. Jacket 19®.6 to 20®. Air about 33® 0.

Thermometer
No. 6163.

Ooirectlou.

Corrected

Temperature.

i'S

Mean Weight W,

ll*®

Temperature.

Work per
Kilogramme
+ l(»2a

■

-.002

Si!460

8.988

n rrnrfti

-192

10428

260

+ .006

22.562

16.087

476

285

1085S

270

WKSM

....

662

]19KSi

280

+ .010

+ .029

24.789

80 381

1421

1087

11707

290

36.907

87.439

.8.7749

1890

1511

12181

800

+ .019

+ .068

SEMI

44.655

2879

1989

12659

810

38.168

51.848

.6.7896

2860

2865

12985

820

+ .081

+ .118

29.807

59.098

8844

2789

18409

880

66.890

8882

8214

13884

840

+ .048

+ .177

73.724

4828

8688

14258

860

82.774

81.168

.6.8188

4817

4068

14683

860

+ .068

+ .367

88.989

88.462

5811

4488

15108

870

95.784

.6.0166

5807

4918

15588

880

+ .072

+ .861

86.280

6807

5887

15957

890

37.466

110-560

.6.7876

6808

5760

16880

400

+ .087

+ .468

118.121

7811

6187

10807

410

89,831

125.693

U.7808

7815

6614

17284

420

+ .106

+ .596

188.360

)

8831

7040

17660

. . .

7465

18085

7891

18511

. . .

....

8817

18987

TABLE XLVIIL— Twelfth Sbbibs.
Experiment of December 17, 1878.

On the Mechanical Equivalent op Heat

4S5

■0961 +

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« Corrections for 0 point flP.OS C. In the experiments previoiis to this no correction was necessary. « These are interpolated from the

observationa.

4:56

Hbitet a. Ecwxand

TABLB XLIX. — Teibtbbm'tb Bbbibb.

Deo. 19, 1878. Jacket 8o.3 to S^.B. Air 4'’.2 to 8.3 0.

On thb Meohanioal EQTnvALBNT OP Heat

457

TABLE L. — PorrBTBBNTH Sbbibs.

December 20, 1878. Jacket 1®.6 to 1®.9. Air about 8®.4 C.

Temperature
by Kew
Standard.

Time.

Corrections. |

Corrected Tem-
perature Abso-
lute Scale.

Revolution of
Chronograph.
2n.

Mean Weight

W|l

Temperature.

si .

^ 0 4.

111

86.0

60.0

.00

i!82

8.08

7.8682

2287

88.5

68.4

.. . .

—

....

8.28

16.87

7.8468

601

508

2718

41.0

-.01

.00

+ .01

4.62

34.78

7.8705

1206

986

8146

48.5

8.8

....

—

....

6.02

88.19

7.4012

1812

1870

8580

46.0

6.8

-.02

+ .01

+ .04

7.48

41.48

7.4142

2412

1808

4018

48.6

8.2

....

. . . .

8.84

49.81

7.4177

8016

2226

4486

61.0

10.7

-.08

+ .02

+ .09

10.26

68.18

7.4890

8624

3656

4866

68.5

18.2

....

,. . .

• « » •

11.68

66.56

7.4107

4284

8084

5294

56.0

16.6

-.04

+ .08

+ .16

18.12

74.95

7.8498

4842

8518

5728

68.5

18.2

. .. .

.. . ,

...

14.56

88.56

7.8269

5461

8942

6152

61.0

30.7

-.04

+ .06

+ .25

16.01

92.27

7.2885

6085

4869

6579

68.5

28.8

....

—

• . . .

17.46

100.99

7.1608

6708

4790

7000

66.0

26.9

-.06

+ .06

+ .88

18.03

109.95

7.2075

7880

5220

7480

68.6

28.5

. .. .

....

• • • •

20.89

118.84

7.1889

7957

6650

7860

71.0

81.2

-.06

+ .08

+ .62

21.86

127.88

7.2122

8589

6081

8291

78.6

88.8

. . . .

—

. . . .

28.84

186.76

7.2252

9218

0607

8717

76.0

86,5

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+ .10

+ .69

24.84

146.78

7.2184

9857

0985

9145

78.5

89.2

. . . .

20.88

164.80

10498

7864

9674

7791

10001

8219

10429

8648

10858

9074

11284

9490

11709

9925

12136

10852

12562

TABLE LI. — WoBK is KhjOObamhb-Mbtbbs at Baltimobb to Hbat Oistb EHiOGbamiib op Watbb pbom an Unknown

Point to a Given Tbmfbbatubb on thb AbboiiUtb Soalb.

468

Hbnbt a. Eowland

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On the Mbohanioal Equitalent oe Heat

459

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TABLE LII.— Meohajvioaii Equiyai^ent of Heat in Ealoobamme-Metbes at Bai^timobe, eaoh yaltth oai.otjIiAted fbom

A Rise of 10° C. rw Tbmpbbatube.

460

Hbnbt a. Eowlaud

■On the Mbohanioal Equtvalbnt oe Heat

461

425.6

Temperature. | Work. Mechanical Equivalent of Heat.

462

Hbnbt a. Rowland

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On the Meohanioal Equivalent oe Heat

463

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mperatureon the
Aosolute Soale.

464

Henbt a. Rowland

TABLE LIY. — ^Fii^al most Pbobable Bbsxtlts.

TABLE LY.— Quaetitt to Add to the Equivalent at Baltimore to
Reduce to ant Latitude.

Manchester— 0.5 ; Paris — 0.4; Berlin — 0.5.

OiT THE Mbohanioal Eqttt tat.ktt t oe Heat

465

V. CONCLTIDINa BEMAEKS, AND OBITICISM OB’ BESTTLTS AND

MBITEODS

Oh lookiHg over the last four colmnHB of Table LIII, ■which, gives
■the res’alts of the experunents as expressed in terms of the difterent
mercurial thermometers, we cannot but be impressed with the unsatis-
factory state of 'the science of thermometry at the present day, when
nearly all physicists accept the mercurial thermometer as the standard
between 0° and 100*. The wide discrepancy in the results of calori-
metric experiments requires no further explanation, especially when
physicists have taken no precaution with respect to ■ihe change of zero
after the heating of the thermometer. They show that thermometry
is an immensely difficult subject, and that the results of all physicists
who have not made a special study of their thermometers> and a com-
parison ■with the air thermometer, must be greatly in error, and should
be rejected in many cases. And this is specially the case where Qeiesler
thermometers have been used.

The comparison of my o'wn thermometers ■with the air thermometer is
undoubtedly by far the best so far made, and I have no improvements to
offer beyond those I have already mentioned in the ‘ Appendix to Ther-
mometry.’ And I now believe that, with the improvement to the air
thermometer of an artificial atmosphere of constant pressure, we conoid
be reasonably certain of obtaining the temperature at any point up to
60® C. within 0®'01 C. from the mean of two or three observations.
I believe that my own thermometers scarcely differ much more than
that from the absolute scale at any point up to 40® 0., but they represent
the mean of eight observations. However, there is an uncertainty of
0®-01 C. at the 20® point, owing to the uncertainty of the value of m.
But taking m = '00016, 1 hardly think that the point is uncertain to
more than that amount for the thermometers Hos. 6163, 6165, and 6166.

As to the comparison of the other thermometers, it is evidently un-
satisfactory, as they do not read acburately enough. However, the fig-
ures given in Table LIII are probably very nearly correct.

The study of the thermometers from the different makers introduces
the question whether there are my thermometers which stand below the
air thermometer between 0® and 100®. As far as I con find, nobody has
ever published a table showing such a result, although Bosscha infers that
thermometers of ''Oristal de Choisy-le-Eoi” should stand below, and
his itifcronce has been accepted by Ecgnaiilt. But it does not seem
to'have been proved by direct experiment. My Baudin thermometers
seem to contain lead as far as one can tell from the blackening in a gas
30

466

Heitbt a. Eowland

flaiii6/but they stand very much above the air thermometer at 40°. I
have since tried some of the Baudin thermometers np to 300°, and find
that they stand Mow the air thermometer between 100° and ^40° ; they
coincide at about 340°, and stand above between 340° and 300°. This
is very nearly what Eegnanlt found for Verre Ordinaire.'^ It is to* be
noted that the formula obtained from experiments below 100° makes
them coincide at 333°, which is remarkably close to the result of actual
experiment, especially as it would require a long, series of experiments
to determine the point within 10°.

The comparison of thermometers also shows that all thermometers
in accurate investigations should be used as thermometers with arbi-
trary scales, neither the position of the zero point nor the interval be-
tween the 0° and 100° points being assumed correct. The text books
oidy give the correction for the zero point, but my observations show
that the interval between the 0° and 100° points is also subject to a sec-
ular change as well as to the temporary change due to heating. Of
all the thermometers used, the Geissler is the worst in this as in other
respects, except accuracy of calibration, in which it is equal to most of
the others.

The experiments on the specific heat of water show an undoubted
decrease as the temperature rises, a fact which will undoubtedly sur-
prise most physicists as much as it surprised me. Indeed, the dis-
covery of this fact put back the completion of this paper many months,
as I wished to make certain of it. There is now no doubt in my mind,
^d I put the fact fo-rth as proved. The only way in which an error
accountiug for this decrease could have been made appears to me to be
in the detemimation of m in Thermometry.” The determination of
m rests upon the determination of a difference of only 0°-05 0. between
the air thermometer and the mercurial, the 0° and 40° points coincid-
ing, and also upon the comparison of the thermometers with others
whose value of m was known, as in the Appendix. Although the quan-
tity to be measured is small, yet there can be no doubt at least that fa
is larger than zero; and if so, the specific heat of water certainly has a
TTfimiTTmnn at about 30°.

One point that might he made against the fact is that the Kew stand-
ard, Table L, gives less change than the others. But the calibra-
tion of the Kew standard, although excellent, could hardly be trusted to
0°-02 or 0°-03 C., as the graduation was only to F. In. drawing the
curve for the difference between the Kew standard and the air ther-
mometers, I ignored small irregularitiee and drew a regular curve. On

On ihb Mbohanioal Equivalent oe Heat

467

lookmg over the observations again^ I see that, had I taken accoimt of
the small irregularities, it would have made the observations agree more
nearly with the other thermometers. Hence the objection vanishes.
However, I intend working up some observations which I have with the
Hew standard at a higher temperature, and shall publish them at a
future time.

There is one other error that might produce an apparent decrease in
the specific heat, and that is the slight decrease in the torsion weight
from the beginning to the end of most of the experiments, probably due
to the slowing of the engine. By this means the torsion circle might
lag behind. I made quite an investigation to see if this source of error
existed, and came to the conclusion that it produced no perceptible
effect. An examination of the different experiments shows this also,
for in some of them the weight increases instead of decreasing. See
Tables XXXVn to L.

The error from the formation of dew might also cause an apparent
decrease; but I have convinced mysdf by experiment, and others can
convince themselves from the tables, that this error is also inappre-
ciable.

The observations seem to settle the point with regard to the specific
heat at the 4° point within reasonable limits. There does not seem
to be a dbange to any great extent at that point, but the specific heat
decreases continuously through that point. It would hardly be possible
to arrive at this so acciuately as I have done by any method of mixture,
for Pfaundler and Platter, who examined this point, could not obtain
results within one per cent, while mine show the fact within a fraction
of one per cent.

The point of minimum cannot be said to be known, though I have
placed it provisionally between 30® and 36® 0., but it may vary much
from that.

The method of obtaining the specific heat of the calorimeter seems
to be good. The use of solder introduces an uncertainty, but it is too
small to affect the result appreciably. The different determinations of
the specific heat of the calorimeter do not agree so well as they might,
hut the error in the equivalent resulting from this error is very small,
and, besides, the mean result agrees well with the calculated result. It
may be regarded as satisfactory.

The apparatus for determining the equivalent could scarcely be im-
proved mu(fii, although perhaps the record of the torsion might be made
automatic and continuous. The experiment, however, might be im-

468

Hbnbt a. Eowiand

proved in two ways; first, by the use of a motive power more regular in
its action; and, second, by a more exact determination of the loss due to
radiation. The effect of the irregularity of the engine has been calcu-
lated aa about 1 in 4000, and I suppose that the error due to it cannot
be as much as that after applying the correction. The error due to
radiation is nearly neutralized, at least between 0° and 30°, by using
the jacket at different temperatures. There may be an error of a small
amount at that point (30°) in the direction of making the mechanical
equivalent too great, and the specific heat may keep on decreasing to
even 40°.

Between the limits of 15° and 35° I feel almost certain that no sub-
sequent-experiments win change my values of the equivalent so much
as two parts in one thousand, and even outside those limits, say be-
tween 10° and 30°, I doubt whether the figures will ever be changed
much more than that amount.

It is my intention to continue the experiments, as well as work up
the remainder of the old ones. I shall also use some liquids in the
calorimeter other than water, and so have the equivalent in tetms of
more than one fiuid.

SaMmort, 1878-79. FinUTud Jfay 37, 1879.

APPENDIX TO PAPER ON THE MECHANICAL EQUIVALENT
OF HEAT, CONTAINING THE COMPARISON WITH DR.
JOULE’S THERMOMETER

{Proceedings of the American Aeadsmy of Arts and Sciences, XVI, 88-46, 1881]
Presented, March, 1880

In the body of this paper I have given an estinaate of the departure of
Dr. Jonle^s thermometer from the air thermometer, based on the com-
parison of thermometers of similar glass. But as it seemed important
that the classical determinations of this physicist should be reduced to
some exact standard, I took to England with me last snxmner one of
my standards, — ^Bandin, No. 6166 , — and sent it to Dr. Jonle with a
statement of the circumstances. He very kindly consented to make
the comparison, and I now have the results before me. These confirm
the estimate that I had previously made, and cause our values for the
equivalent to agree with great accuracy. The following is the table of
the comparison: —

Readings.

Temperatures.

Baudin, No. 6166.

Joule.

By perfect Air
Thermometer
according to
No. 6 m

By Joule's
Thermometer.

Blfforonoe.

21.88

22.62

41.980

69.410

1.690

1.678

-.012

48.782

72.200

2.126

2.127

+ .001

68.706

81.840

2.611

2.619

.008

68.916

90.877

2.918

2.928

64.914

101.777

8.882

8.896

.014

78.874

117.291

4.089

4.061

80.176

129.990

4.667

4.606

.089

85.268

189.266

4.961 ,

6.008

.042

90.664

148.884

6.870

6.414

.044

94.248

166.460

6.664

6.698

.044

99.168

164.400

6.086

6.082

.046

104.080

178.140

6.418

6.467

.044

108.868

182.040

6.789

6.889

118.706

190.886

7.166

7.218

.068

114.000

191.882

7.188

7.289

.061

n 2 l .507

»219.497

17.772

18.446

...

1 Bvidently a mlstalEe in the readings.

470

Hbitbt a. Eowland

Conti^vued,

Headings.

Tempeiatures.

Baudln, No. 0166.

Joule.

By perfect Air
O^erxnometer
according to
No. eiS.

By Joule’s
Thermometer.

Blllerenoe.

186.858

231.116

8. §90

8. §44

.§64

140.467

289.989

9.249

9.809

.060

148.405

216.006

9.479

9.540

.061

146.445

260.666

9.717

9.778

.061

152.860

261.481

10.180

10.246

.066

168.770

278.289

10.681

10.761

070

164.685

288.967

11.188

11.311

.073

170.486

294.789

11.695

11.670

.076

175.486

808.682

11.979

12.067

.078

182.796

816.968

12.560

12.627

.077

188.705

827.746

18.008

18.089

.081

108.954

887.220

18.412

18.495

.083

199.558

817.294

18.844

18.928

.084

206.054

269.060

14.848

14.482

.089

211.628

868.958

14.764

14.857

.093

216.440

877.826

16.142 -

16.887

.095

221.858

887.562

16.660

15.666

.095

229.601

401.419

16.168

16.249

.091

285.598

412.867

16.628

16.719

.096

241.028

422.268

17.046

17.148

.098

247.486

483.800

17.641

17.688

.097

258.704

446.^67

18.028

18.180

.102

259.786

456.286

18.600

18.608

.108

266.086

467.817

19.991

19.097

.106

278.148

480.648

19.689

19.648

.109

280.176

498.442

20.086

20.197

.111

287.684

506.906

20.666

20.774

.108

294.927

520.052

21.282

21.888

.106

804.148

586.882

21.947

22.058

.111

810.397

648.162

22.482

22.544

.113

816.596

559.886

22.916

28.028

.107

821.271

668.051

28.282

28.897

.115

827.148

678,528

28.742

28.840

.104

888.661

690.661

24.261

24.867

.116

889.664

601.696

24.719

24.886

.117

846.557

614.004

25 .254

25.869

.115

852.878

625.610

26.746

25.862

.116

859.986

638.526

26.299

26.421

.122

865.080

647.888

26.697

26.820

.128

871.811

660.071

27.225

27.845

.130

882.770

680.149

28.087

28.206

.119

We can discuss the comparison of these thermometers in two ways;
either hy direct comparison at the points we desire, or by the repre-
sentation of the differences hy a formula.

Joule’s result in 1850 was referred to water at about 14® C., and in
1878 to water at 16®-5 0. Taking interrals in the above table of from

ApPEITDIX to the MbOHANIOAL EQTHVALBMrT OP TTtbat . 471

6° to 12®, so that the mean shall he nearly 14° and 16°-6, 1 find the
following for the ratios : —

1-0044

1-0042

1-0049

1-0040

1-0047

1-0030

1-0047

1-0036

1-0062

1-0036

Mean, 1-0047

1-0037

So that we have the following for Joule’s

old and hew values: —

Old.

New.

423-9

Correction for thermometer

2-0

1-6

Correction for latitude

•5

•6

Correction for sp; ht. of copper

•7

427-1

426-0

My value

427-7

427-1

DifiEerence

•6

1-1

or 1 in. 700 and 1 in 390, respectively.

But the correction found in this way is subject to local irregulari-
ties, and it is perhaps better in many respects to get the equation giving
the temperature of Joule’s thermometer on the air thermometer. Let
T be the temperature by Joule’s thermometer, and t that by the air
thermometer. Then I have found

i = 0-002 + 1-00126 T— •00013 |l00 — (100 + r)f

The factor 1-00126 enters in the formula, probably because the ther-
mometer which Joule used to get the value of the divisions of his ther-
mometer was not of the same kind of glass as his standard. The rela-
tive error at any point due to using the mercurial rather than the air
thermometer will then be

= 1 —00126 + -00000039 \ 23300 — 666 < -f 3 j-

472

Hbnet a. Rowland

From this I have constructed the following table: —

Temperature.

Approxlxuate Addition to Equivalent}
as measured on Joule’s Thermometer.

Hetrio System.

English System.

.0078

8.8

6.0

.0066

2.8

5.1

.0054

2.8

4.2

.0042

1.8

8.2

.0081

1.8

2.4

,0021

1.6

.0011

Corrected in this way we have, —

Old.

Nevr.

Joule’s value

423-9

Beduction to air thermometer

1-9

1-7

Beduction to latitude of Baltimore

-6

•6

Correction for sp. ht. of copper

-7

427-0

426-1

My value

427-7

427-1

Difference

■7

1-0

or 1 in 600 and 1 in 426, respectively.

But it is evident that all the other temperatures used in the experi-
ment must also be corrected, and I have done this in the following man-
ner. The principal other correction required is in the capacity of the
calorimeter, and ihis amounts to considerable in the experiments on
mercury and east-iron, where no water is used. Dr. Joulo informs mo
that the thermometer with which he compared mine was made in 1844,
but does not give any mark by which to designate it, although it is evi-
dently the thermometer called "A” by him. I shall commence with the
experiments of 1847. The calorimeter was composed of the following
substances, whose capacities I recompute according to what in my paper
I have considered the most probable specific heats.

Water

Brass

Copper

Tin

Weight.
77617 grains
24800 grains
11237 grains
(?)

Capacity aocwd- Most pxol>ablo Most probable
mg to Joule. BpeolfloHeat. Capacity.

77617 1-000 77617

2319 -0900 2232

1066 -0922 1036

363 .... 863

Total capacity 81355

81248

Appendix to the Meohanioal EQtrrvAiENT op Heat 473

Equivalent found

781-6

Correction for thermometer

3-3

Correction for capacity

1-3

Correction for latitude

-9

Corrected value

787-0

or 448 • 8 at 16® 0. on the air thermometer.

The other experiment, on sperm oil, made at this time, is probably
hardly worth reducing. The experiments of 1850 are of the highest
importance and should be accurately reduced.

In the experiments with water the capacity of the calorimetar is cor-
rected as follows: —

Wetftht. Oi^oltyused Most probable Most probable
by Joule. SpeolfloHeat. Capacity,

Water 93889-7 93889-7 1-000 93889-7

Copper 86541- 8430-8 -098 8349-8

Brass 18901- 1800-0 -091 1780-0

Brass stopper 10-3 .... 10-3

Total capacity 97470-8 97309-8

Hierefore correction is -001.6.

Hence the result with water requires the following corrections: —

Joule’s value

Correction for thermometer
Correction for latitude
Correction for capacity

778-7 at 14® C.

•9

1-8

778-0

or 486-8 on the air thermometer in the latitude of Baltimore at the
temperature of 14® C., nearly.

In the next experiment, with mercury. Joule determined the capacity
of the apparatus by experiment. The mean of the experiments was that
the apparatus lost 80® - 33166 F. in heating 143430 grains of water
3® -13306 F. To reduce these to the air thermometer we must divide
respectively by 1-0048 and 1-0056. Therefore the capacity must be
divided by 1-0014. Therefore the corrected values are: —

778-8 at 9® C. 776-4 at 11® C.

Correction for thermometer

4-4

4-0

Correction for capacity

1-1

Correction for latitude

•9

-9

779-8

7814

474

HaNitT A. Eowlakd

The reduction, to the air thermometer waB made for the temperatures
of 9° C. and 11® C. respectively, but they both refer to the temperature
of the water used when the capacity was determined; this was about
9® C. Hence these experiments gave 497"6 and 488'7 on the air ther-
mometer, with the water at about 9® 0.

The next expeiiments, with cast-iron, can be corrected in the same
manner, and thus become

. 776-0

773-9

Correction for thermometer

4-9

4-3

Correction for capacity

1-1

Correction for latitude

-9

789-9

780-9

and these are as before for water at 9®.

The determination by the heating of a wire, whose resistance was
measured in ohms, can be thus reduced. The value found by Joule
was 499-9 in the latitude of Baltimore at 18®'6 C.

Using the capacity of the copper -0999, as I have done in my paper,
this quantity be increased to 430-3. But I have given reasons in
my paper on the “ Absolute Unit of Electrical Eesistance ” to show that
there should be a correction to the B. A. Committee’s experiments,
whidb would make the ohm -993 earth quadrant second, instead of
1-000 as it was. meant to be, which nearly agrees with the quantity
which I found, namely, -991. Taldng my value -9911, Joule’s result
will reduce as follows: —

Correction for thermometer
Correction for capacity
Corrected for ohm

499.9 at 18®-6 0.
-hl-6
+ -4
— 3-8

Corrected value

498-0 at 18®-6 C.

The last determinations in the ‘ Philosophical Ttansactions ’ of 1878
can be reduced as follows :

The capacity of the calorimeter was determined by experiment, in-
stead of calculated from the spedflc heat of copper given by Eegnault,
as in the older experiments. The value used, 4849-4 grains, corre-
sponded to a specific heat of brass of about -090, which is almost exactly
. what I have considered right. The reduction to the air thermometer
will decrease it somewhat, and the correction for the increase of the

Appendix to the Mboeanioai Equivalent op Heat 476

specdfio heat of brass and the decrease of the specifLo heat of water wUl
also change it somewhat. la all, the amount will be about 1 in 200.
Hence the reduction becomes as follows :

Joule’s values

772-7

774-6

773-1

767-0

774-0

Correction for thermometer

3-2

3-7

3-1

3-3

2-8

Correction for capacity

•2

-2

Correction for latitude

•9

-9

Correction to vacuum

— •9

Corrected values

776-1

778-6

776-4

770-5

777-0

at 14**7 atia®-? atl2®-6 at 14'»*5 at 17“-8

To reduce the values in English measure to metres and the Centi-
grade scale, I have simply taken the redueiag factor 1*8 )< •304794,
although the barometer on the two systems is not «actly the same:
for this is taken into account in the comparison of the thermometers.
However, a barometer at 30 in. and 60® E. is equivalent to 759'86 mm.
at 0® C. which hardly makes a difEerenee of 0®-01 0. in the temperature
of the hundred-degree point.

No.

Date.

Method.

Tem.

water.

Joule's

Value.

Joule's Value re-
duced to Air Theiy
momoter and T^ati-
tude of Baltimore.

Howland's

Value.

J.-

-11.

English

measure.

Metric

system.

1847

Friction of water

781.6

787.0

442.8

437.4

+ 16.4

1850

water

772.7

778.0

426.8

427.7

—

<«

mercury

772.8

770.3

427.6

438.8

—

1.8

((

mercury

775.4

781.4

428.7

428.8

—

iron

776.0

783.3

430.1

428,8

iron

778.9

780.8

428.0

438.8

....

1867

Bleotric heating

18.0

428.0

426.7

1.8

1878

Friction of water

14.7

772.7

776.1

425.8

427.6

—

1.8

12.7

774.6

778.5

427.1

428.0

—

15.6

778.1

776.4

426.0

427.8

1.8

! 6

14.5

767.0

770.5

422.7

427.6

—

4.8

1 1

17,8

774.0

777.0

426.8

426.9

; 1

In combining these so as to got at the true difference of J oule’s and
my result, we must give these different determinations weights accord-
ing to their respective accuracy, especially as some of the results, as
Ho. 11, have very little weight. Joule rejected quite a number of his
results, but I have thought it best to include them, giving them small
weights, however. In this way we obtain a value for J oule^s experiment

476

Hbney a. Rowland

of 436-76 at 14° ^6, my value at this point being 427-53. The difference
amounts to 1 in 660 only. Giving the observations equal weight, this
would have been 1 in 430 nearly. The quantity 436-75 is what I find
at 18° 0. So that my result at this particular temperature differs from
that of Joule only the amount that water changes in specific heat in
3°-4 C.

Joule^s value is less than my value to the amount given, but the value
from the properties of air, 430-7 at 14° C. is greater, although the
method can have little weight.

It might be well. to diminish my values by 1 part in 1000 so as to make
them represent the mean of Joule^s and my own experiments. It is
seen that the experiment by the method of electric heating agrees very
exactly with the other experiments, lecause I "have reduced it to my value
of the oTirri. Hence I regard it as a very excellent confirmation of my
value of that unit.

Baltimore^ Felruary 16 , 1880 .

PHYSICAL LABOEATOEY: COMPAEISOHS OF STANDAEDS

ilohiM Hopkim TTniver^ty Circular No. 8, p. 81, 1880]

In order to secure uuifonuily throughout the country in certain
physical standards, and to facilitate the use of the absolute system of
heat measurement, it has been thought advisable to organize in the
physical department of this Univereiiy a sub-department, vhere com-
parisons of standards can be made.

Comparison of Thermometers . — ^At present vre are only able to make
comparisons of thermometers, and so to reduce their degrees to the abso-
lute scale of the perfect gas thermometer.

As the "work is very laborious, it is proposed to make this sub-depart-
ment self-supporting, by a system of fees sufficient to cover the bare cost
of the labor, so that all may avail themselves of the facilities here
offered.

In a recent study of standard thermometers by Geissler, Baudin,
Pastr6, Casella and from Kew, and the comparison of the same vrith
the air thermometer, the differences due to the varieiy of the glass
amounted to 0®- 8 or 0®- 3 0., and the differences from the air thermom-
eter were as high sometimes as 0®-3 0. at ihe 40° point.

The error from using unoompared mercurial thermometers in calori-
metric iuvestigations may amount to one or two per cent. For this
reason the air thermometer has been taken as the standard, and all com-
parisons will be reduced to the final absolute standard of the perfect
gas thermometer.

Very complete studies of thermometers have been made between
0° 40° 0., and a less complete study between 0° and ,100°, and be-

tween 100° and 860°. TJp to 100' our thermometers have not only been
compared with the air thermometer, but also witih standards by Fastr4,
Geissler, Casella, Baudin and from Kew.

The study from 0° to 40° has been published by tlie American Acad-
emy of Sciences, at Boston, in a memoir on the Mechanical Equivalent
of Heat. One of our thermometers is also now in the hands of Dr.
Joule, who has compared it with the original thermometers used by him
in the determination of the Mechanical Equivalent of Heat.

478

Heott a. Eowland

The apparatus for the comparison up to 100° C. is described in the
paper above referred to. The thermometers are totally immersed in
the water with their stems very near the bulbs of the air thermometers.
From 100° up to 250° an oil bath is used^ the bulbs only being in the
oil, but the stems are heated to the same degree by being in contact with
a heavy copper bar, whose temperature i^ noted by separate thermome-
ters.

The ordinary comparison is made with the stems of the thermometers
in a vertical position. Where they are used in a horizontal position a
correction will have to be made, and this correction will be determined
when it is so desired. When the comparison is made only to 40°, we
can compare them in a horizontal position, but we cannot then insure
the same accuracy as when they are vertical, and it is never advisable to
use them in that position.

Where desired, a study will be made of the changes of the zero point
as a function of the temperature to which it has been heated, and of the
time, but this study is not advised, as it does not'lead to very valuable
results.

Thermometers with metal, wooden or paper scales are generally too
poor to be worth comparison, and would often be spoiled by the immer-
sion in the water. Thermometers with metal caps of Geissleris form
are often injured, especially when heated to 260° C. Therefore, com-
parisons of thermometers of these classes will not be undertaken, ex-
cept in the case of standards long used for some particular purpose, or
in that of fine Geissler thermometers.

■ Three intervals for the comparison have been selected.

A. Between 0° and 40° for thermometers used for meteorological
observations, determination of the temperature of standards of length,
calorimetric determinations, and all purposes where extreme accuracy is
desired within that l imit . To obtain the full value of such a compari-
son, thermometers should be graduated at least as fine as 0°*1 0. or
0°-2F.

B. Between 0° and 100° 0. It is advised that the thermometers Sent
be graduated at least as fine as 0°-2 C. or 0°*6 F.

C. Between 100° and 250° for thermometers used by chemists in the
determination of melting or boiling points. Thermometers should be
graduated to 1° C. or 1° F.

Three kinds of comparison will be made for each of the intervals
0° to 40°, 0° to 100°, and 100° to 260°, as follows:

1st. Direct comparison with the air thermometer, and also a primary

Physical LAsoitATOET: Compakesohs op Stahdaeds

standard. This comparison is very laborious, and is not recommended
except in very exceptional cases, as more than one comparison should
be made to insure good results.

2nd. Comparison with primary standards which have been compared
many times with the air thermometer. This is recommended where an
error of is of some importance.

3rd. Comparison with secondary standards which have been com-
pared many times with the primary standards, and not very often
directly with the air thermometer. This is recommended in aU ordi-
nary cases, where an error of yJit® can be tolerated.

When several comparisons are made, the following intervals will be
allowed between the experiments, so that the zero reading may be
allowed to return to its primitive value.

Thermometers heated to 40° C. about 1 week.

Thermometers heated to 100° C. about 6 weeks.

Thermometers heated to 260° C. about 4 months.

The latter interval, is too small for an accurate return.

For the exact details of the method of comparison, I must refer to the
above mentioned paper on the Mechanical Equivalent of Heat.

It is advisable in all cases where great accuracy is desired, that a
numbers of comparisons be made, seeing that delicate thermometers are
constantly varying through slight limits, and the average state can only
be determined by repeated experiments.

Reports . — ^In the report of the comparison, the original readings will
be given together with the reduced ones, and the plot of the curve of
errors of the thermometer at every point. From this curve, the error
of the thermometer at any reading can be found.

It is proposed to publish at the end of the year a complete report of
all the comparisons made during the year, together with all new deter-
minations of the errors of the standards, and to send it to any address
at a price which we will hereafter announce.

Fees . — The comparators allow five thermometers only to be placed in
them, of which two are our own standards in ordinary comparisons,
and one in direct comparisons with the air thermometer. Therefore,
three thermometers can be compared as easily as one in ordinary cases,
and four in direct comparisons. Hence the following system of fees
has been made out.

480

Henut a. EowiiAnd

A. Whm a mmiber of Thermometers are sent
Comparison between 0° and 40“ C. for 3 or 4 thermometers.

Direct, probable error at each point =TJTr°

Primary Standards, probable error at each point 11 00

Secondary Standards, probable error at each point = 8 00

0“ and 100“ for 3 or 4 thermometers.

Direct, probable error at each poipt ==.j^“ $35 00

Primary Standards, probable error at each point =- 3 ^°
Secondary Standards, probable error at each point =-j^“ 9 00

100“ to 360“ for 3 or 4 thermometers.

Direct, probable error at each point = yV*

Primary Standards, probable error at each point == 13 00

Secondary Standards, probable error at each point — 9 00

B. For Single Thermometers

For single thermometers, the fees for the direct comparisons should
be reduced to one-third, and for the ordinary ones to one-half the
above figures. But in this case the thermometer will have to remain
here until enough accumulate to fill the comparators.

Directions for Sending. — ^With each thermometer, send the name of
maker, the date when made, purpose for which it is used, and the
highest temperature to which it has lately been heated, and the date
of such heating, together with the kind of comparison desired, and
whether the thermometer is generally used in the horizontal or the
vertical position.

In packing, the thermometer should be placed in a small box, which
should again be packed with straw in a larger box.

The thermometers, both during transit and while here, rdust be at
the owners’ risk. Only sufficient fees have been charged to cover the
bare cost of the comparison, and we bear the risk of our own standards,
which are probably more valuable than any of those which will be sent
to us. But every care will be taken, and the probability of an accident
is very small.

We expect soon to be able to make other comparison^ and notice will
then be given of the fact by the issue of another circular.

ON" GKISSLKR TI[EIIM()MKTKRS: REMARKS BY TROFESSOR
ROWLAND ON THE PRECEDING LETa'ER/ IN A (COMMU-
NICATION DATED JOHNS HOPKINS UNIVERSITY, APRIL
29, 1881

[awwicon Journal afScUuet [«1, XXl, 481-458, 18811

Through tho kindnoas of Dr. Widdo, I have been allowed to boo the
above and would like to givo a fow words of explanation.

In reading what I had to aay with respect to the Goiaslor thermom-
eter, the reader should remember tliat I was not writing on general
thermometry, but only on that part which should be useful to mo in
measuring differeum of temperature within the limits of 0® and 46® 0.
And so I merely made a study of thermometers, their change of zero
and other points, as it affected tho problem which I had before me. I
am well aware that there are formulas for giving the changed readings
of thermometers duo to previous heating, but, according to well known
principles in such casou, I preferred to eliminate sucdi error by tho
proper use of the thormomoter rather than trust to an uncertain theory.

In the course! of my investigation I discovered tho fact that tho
Geissler thermometers, eHp(!cialIy tho one I then used, departed more
from the air thermometer than any other. Now the QeiR8l(!r ther-
mometer has been used for many years by physicists, principally Gor-
man, without any reduction to the air thormomoter. And this correc-
tion was so groat, amounting to over 0®-3 ()., for tho specimen I used, at
tho 45® point, that I thought it right to call attention to tho point.
And I acknowledge that the picture was primont in my mind of a physi-
cist reading a thormomoter from a distance by a tolosoope to avoid the
heat of tho body and parallax, and recording his results to thousandth
of a degree, and all this on a thermometer having an error of 0®<3 0.1
As Dr. Thiesen remarks: If one is to compare his thermometer with
tlie air thermometer, the amount of corr(*(!tion is of little importance:
l)ut departure from the air th«!nnomett‘r is certainly not a recommenda-
tion and, indeed, must introduce sliglit errors. Tho most accurate

' [By Dr. M. Tblcsen, replying tn Rowland’s criticisms of tho Oslssler thermomstsri,
SI oxproHsod lit Ills niomolr < On the Mechanical Kqiilvalent of tleat.’)

48a

Henrt a. Sowland

readings which one can make on an air thermometer will vary several
h-nudredths of a degree.

Hence we can never use with accuracy the direct comparison with the
air thermometer but must express the difference of the two instruments
by some formida of the form:

A Ot ht + &c.

Should we take an infinite number of terms this formula would ex-
press all the irregularities of our observations. But by limiting the
number of terms the curve of differences becomes smoother and
smoother and the formula expresses less and less the irregularities of
the experiment. The number of terms to be used is a matter of judg-
ment, and this point I sought to determine by the use of the observa-
tions of Eegnault and others. The rejection of the higher powers of i
is more or less of an assumption founded on the fact that we are
reasonably certain that the curve of differences between the mercurial
and the air thermometer is a smooth curve. It is evident that the
less the correction to be introduced the less the rejection of the higher
powers of i will affect our results.

We now come to my criticism of the Geissler thermometer for not
having a reservoir at the top. Dr. Thiesen has in some way misunder-
stood my principal reason for its presence. My reason was not that
es vermindert Schadlichkeit der im Quecksilber zuruckgebliebenen
Spuren von Luft ” but that only by its use can the mercury in the bulb
be entirely free from air. Take a thermometer and turn it with the
bulb on top. If the thermometer is large, in nine cases out of ten the
mercury will separate and fall down: allow it to remain and observe the
bubble-like vacuum in the bulb. Turn the bulb in various directions so
as to wash the whole interior of the bulb, as it were, and then bring
the thermometer into a vertical position, Iceeping the bubble in sight.
As the mercury flows back, the bubble diminishes and finally, in a good
thermometer, almost disappears: but in most thermometers a good
sized bubble of air, in some cases as large as the wire of a pin, remains.
It is the most important function of a reservoir at the top to permit
such manipulations as to drive all such air into the top reservoir and to
make the mercury and the glass assume such perfect contact that the
bulb can be turned uppermost witho-ut the mercury separating, even in
thermometers of large size and with good generous bulbfe. In many
Geissler thermometers such a test might succeed, not on account of the
freedom from air, but because the capillary tube and bulb are so small

On the Geissler Thermometers

483

and the coliinin so short that the capillary action is sufficient to prevent
the fall. Now I think that a thermometer in which there is this layer
of air around the mercury in the bnlb must be uncertain in its action;
hence my opinion is unaltered that all thermometers in which we can-
not remove this layer or at least make certain of its absence should be
rejected.

Furthermore, with respect to calibration, the reservoir is not essen-
tial to the calibration of thermometers whose range is 0® and 100® C.
Jlut my remarks ajjply bettor to those whose range is between 0® and
30® C. or 40® 0. Here calibration is impossible with a short column
at ordinary temperatures unless some of the mercury can be stored up
in the reservoir so as to allow the col umn to move over the whole scale.
And it is within this limit that thermometers are of the greatest value
in the physical laboratory.

The other defects of the Geissler thermometer, the scale which was
always coming loose, the metal cap which was never tight and always
allowed water to enter, the small capillary tube which wandered with
perfect irregularity from side to side over the scale, all these were so
obvious that I confined my remarks to the more obscure errors.

Furthermore, I believe there is some error in most Geissler ther-
mometers from the small size of the bulb and the capillary tube, and
this I have mentioned on p. 124* of the paper referred to. Pfaundler
and Platter, in a paper on the specific heat of water, in Poggendorff^s
Annalen for 1870, found an immense variation within small limits. In
a subsequent paper * the authors traced this error to the lagging of the
thermometer behind its true reading.

The authors xased Geissler thermometers graduated to -jj^® 0. 1 in a
series of experiments mode by plunging the thermometer into water
after slightly heating or cooling the thermometer so that *in one case
the mercury fell and the other rose to the required point. When the
thermometer fell about 6® or 8® 0. it lagged behind 0®*0664 and when
it rose 3® or 4® it lagged 0® -022, making a difference of 0® -087 C. ! Now
my thermometers made by Baudin show no effect of this kind. They
indicate accurately the temperature whether they rise or fall to the
given point, provided the interval is not too great. The fact then
remains that a Geissler thermometer graduated to C. may be uncer-^
tain to 0®-087C., while a Baudin graduated to mm., one mm. being
from tV® to tV® C. is not uncertain to 0®*01 or 0®-02 0. May not the

1 [p. 898 this volume.!

•Poggendorff’8 Annalen^ exU, p. 687.

484 :

Hbnbt a. Eowland

catiBe be fouad in the layer of air around the mercury of the bulb
which cannot be removed without a reservoir at the top ? Or may we
not also look for such an effect from the minute size of the bore of the
capillary tube which creates a different pressure in the bulb from a
rising or falling meniscus? Possibly the two may be combined.

PART IV

LIGHT

PBELIMINAEY NOTICE OF THE EESULTS ACCOMPLISHED
IN THE MANUFACTURE AND THEORY OF ORATINGS FOB
OPTICAL PURPOSES

[aToAnt SopJeiM Univertity Oireulan, £fo. 17, pp. 348, 349, 1883 ; jPMlowpMecA Hagatint
[4], Xni, 469-474, 1888; NcOure, 36, 311-318, 1883; Journal Oe nyiigut,

II, 6-11, 1888]

It is not many years since physicists considered that a spectroscope
constructed of a large number of prisms was the best and only instru-
ment for viewing the spectrum, where great power was required. These
instruments were large and expensive, so that few physicists could pos-
sess them. Professor Young was the first to discover that some of the
gratings of Mr. Rutherfurd showed more than any prism spectroscope
which had then been constructed. But all the gratings which had been
made up to that time were quite small, say one inch square, whereas
the power of a grating in resolving the lines of the spectrum increases
with the size. Mr. Rutherfurd then attempted to make as large grat-
ings as his machine would allow, and produced some which were nearly
two inches square, though he was rarely successful above an inch and
three-quarters, having about thirty thousand lines. These gratings
were on speculum metal and showed more of the spectrum than had
ever before been seen, and have, in the hands of Young, Rutherfurd,
Lockyer and others, done much good work for science. Many mechanics
in this country and in France and Germany, have sought to equal
Mr. Rutherfurd’s gratings, but without success.

Under these circumstances, I have taken up the subject with the
resources at command in the physical laboratory of the Johns Hopkins
Universiiy.

One of the problems to be solved in making a machine is to make a
perfect screw, and this, mechanics of all countries have sought to do
for over a hundred years and have failed. On thinking over the matter,
I devised a plan whose details I shall soon publish, by which I hope to
make a practically perfect screw, and so important did the problem seem
that I immediately set Mr. Schneider, the instrument maker of the
university, at work at one. The operation seemed so successful that I

488

Hbnry a. Eowland

immediately designed the remainder of the machine, and have now had
the pleasure since Christmas of trying it. The screw is practically per-
fect, not by accident, but because of ihe new process for making it, and
I have not yet been able to detect an error so great as one one-hnndred-
thonsandth port of an inch at any part. Neither has it any appreciable
periodic error. By means of this machine I have been able to make
gratings with 43,000 lines to the inch, and have made a ruled surface
with 160,000 lines on it, having about 29,000 lines to the inch. The
capacity of the machine is to rule a surface 6Jx4i inches with any
required number of lines to the inch, the number only being limited by
the wear of the diamond. The machine can be set to almost any num-
ber of lines to the inch, but I have not hitherto attempted more than
43,000 Lines to the inch. It ruled so perfectly at this figure that I see
no reason to doubt that at least two or three times that number might
be ruled in one inch, though it would be useless for making gratings.

AU gratings hitherto made have been ruled on flat surfaces. Such
gratings require a pair of telescopes for viewing the spectrum; these
telescopes interfere with many experiments, absorbing the extremities
of the spectrum strongly; besides, two telescopes of sufl&cient size to
use with six inch gratings would be very expensive and clumsy affairs.
In thinking over what would happen were the grating ruled on a sur-
face not flat, I thought of a new method of attacking the problem, and
soon found that iE the lines were ruled on a spherical surface the
spectrum would be brought to a focus without any telescope. This
discovery of concave gratings is important for many physical investiga-
tions, such as the photographing of the spectrum both in the ultra-
violet and the ultrarred, the determination of the heating effect of the
different rays, and the determination of the relative wave lengths of
the lines of the spectrum. Furthermore it reduces the spectroscope to
its simplest proportions, so that spectroscopes of the highest power may
be made at a cost which can place them in the hands of all observers.
With one of my new concave gratings I have been able to detect double
lines in the spectrum which were never before seen.

The laws of the concave grating are very beautiful on account of their
simplicity, especially in the case where it will be used most. Draw the
radius of curvature of the mirror to the centre of the mirror, and from
its central point with a radius equal to half the radius of curvature
draw a circle; this circle thus passes through the centre of curvature
of the mirror and touches the mirror at its centre. Now if the source
of light is anywhere in this circle, the image of this source and the

Geatings for Ortioal Pttbposes

489

different orders of the spectra are all brought to focus on this circle.
The vord focus is hardly applicable to the case, however, for if the
source of light is a point the light is not brought to a single point on
the circle but is drawn out into a straight line witii its length parallel
to the axis of the circle. As the object is to see lines in the spectrum
only, this fact is of little consequence provided the slit which is the
source of light is parallel to the axis of the circle. Indeed it adds to
the beauty of the spectra, as the horizontal lines due to dust in the slit
are never present, as the dust has a different focal length from the lines
of the spectrum. This action of the concave grating, however, some-
what impairs the light, especially of the higher orders, but the intro-
duction of a cylindrical lens ^eatly obviates this inconvenience.

The beautiful simplicity of the fact that the line of foci of the dif-
ferent orders of the spectra are on the circle described above leads
immediately to a mechanical contrivance by which we can move from
one spectrum to the next and yet have the apparatus always in focus ;
for we only have to attach the slit, the eye-piece and the grating to three
arms of equal length, which axe pivoted together at their other ends
and the conditions are satisfied. However we move the three arms the
spectra are always in focus. The most interesting case of this contriv-
ance is when the bars carrying the eye-piece and grating are attached
end to end, thus forming a diameter of the circle with the eye-piece at
the centre of curvature of the mirror, and the rod carrying the slit
alone movable. In this case the spectrum as viewed by the eye-piece
is normal, and when a micrometer is used the value of a division of its
head in wave-lengths does not depend on the position of tire slit, but
is simply proportional to the order of the spectrum, so that it need be
dotermined once only. Furthermore, if the eye-piece is replaced by a
photographic camera the photographic spectrum is a normal one. The
mechanical means of keeping the focus is especially important when
investigating the ultra-violet and ultra-red portions of the solar
spectrum.

Another important property of the concave grating is that all the
Bupenmposed spectra arc in exactly the same focus. When viewing
such superimposed spectra it is a most beautiEul sight to see the lines
appear colored on a nearly white ground. By micrometric measurement
of such superimposed spectra we have a most beautiful method of
determining the relative wave lengths of the different portions of the
spectrum, which far exceeds in accuracy any other method yet devised.
In working in' the ultra-violet or ultra-red portions of the spectrum we

490

Hbkbt a. Rowland

can also focus on the snperimposed spectruin and so get the focns for
the portion experimented on.

The fact that the light has to pass through no glass in the concave
grating makes it important in the examination of the extremities of
the spectrum where the glass might absorb very much.

There is one important research in which the concave grating in its
present form does not seem to be of much use, and that is in the exami-
nation of the solar protuberances; an instrument can only be used for
this purpose in which the dust iu the slit and the lines of the spectrum
are in focus at once. It might be possible to introduce a cylindrical
lens in such a way as to obviate this difficulty. But for other work on
the sun the concave grating will be found very useful. But its principal
use will be to get the relative wave lengths of the Hues of the spectrum,
and so to map the spectrum; to divide lines of the spectrum which are
very near together, and so to see as much as possible of the spectrum;
to photograph the spectrum so that it shall be normal; to investigate
the portions of the spectrum beyond the range of vision; and lastly to
put in the hands of any physicist at a moderate cost such a powerful
instrument as could only hitherto be purchased by wealthy individuals
or institutions. ,

To give further information of what can be done in the way of grat-
ings I will state the following particulars:

The dividing engine can rule a space 6i inches long and 4i inches
wide. The lines, which can be 4i inches long, do not depart from a
straight line so much as - n r o^ooo hich, and the carriage moves forward in
an equally straight line. The screw is practically perfect and has been
tested to j o o^od t i^ch without showing error. Neither does it have any
appreciable periodic error, and the periodic error due to the mounting
and graduated head can be entirely eliminated by a suitable attachment.
For showing the production of ghosts by a periodic error, such an error
can be introduced to any reasonable amount. Every grating made by
the machine is a good one, dividing the 1474 line with ease, but some
are better than others. Eutherfurd^s machine only made one in every
four good, and only one in a long time which might be called first-class.
One division of the head of the screw makes 14,438 lines to the inch.
Any fraction of this number in which the numerator is not greater
than say ^0 or 30 can be ruled. Some exact numbers to the millimetre,
such as 400, 800, 1200, etc., can also be ruled. For the finest definition
either 14,438 or 28,876 lines to the inch are recommended, the first for
ordinary use and the second for examining the extremities of the

G-baxin-gs xob Optical Pttkposbs

491

spectrum. Eztremdy brilliant gratings bave been made with 48,314
lines to the inch, and there is little difficulty in ruling more if desired.
The follouring show some results obtained:

Flat grating, 1 inch square, 43,000 lines to the inch. Divides the
line in the first spectrum.

Plat grating, 3X3 inches, 14,438 lines to the inch, total 43,814.
Divides 1474 in the first spectrum, the E line (Angstrom 6269-4) in
the second and is good in the fourth and even fifth spectrum.

Flat grating, 2X8 inches, 1200 lines to one millimetre. Shows very
many more lines in the B and A groups than were ever before seen.

Plat grfcting, 2 X 3i inches, 14,438 lines to the inch. This has most
wonderful brilliancy in one of the first spectra, so that I have seen
the Z line, wave-length 8240 (see Abney’s map of the ultra-red regio'n),
and determined its wave-length roughly, and have seen much further
below the A line than the B line is above the A line. The same may
be said of the violet end of the spectrum. But such gratings are only
obtained by accident.

Concave grating, 2X3 inches, 7 feet radius of curvature, 4818 lines
to the inch. The coincidences of the spectra can be observed to the
tenth or twelfth spectrum.

Concave grating, 2X3 inches, 14,438 lines to the inch, radius of cur-
vature 8 feet. Divides the 1474 line in the first spectrum, the E line
in the second, and is good in the third or fourth.

Concave grating, 3 X SJ inches, 17 feet radius of curvature, 28,876
lines to the inch, and thus nearly 160,000 lines in all. This shows
more in the first spectrum than was ever seen before. ^ Divides 1474
and E very widely and shows the stronger component of Angstrom 6275
dotible. Second spectrum not tried.

Concave grating, 4 X inches, 3610 lines to the inch, radius of cur-
vature 6 feet 4 inches. This grating was made for Professor Langley’s
experiments on the ultra-red portion of the spectrum, and was thus
made very bright in the first spectrum. The definition seems to be
very fine notwithstanding the short focus and divides the 1474 line with
ease. But it is difficult to rule so concave a grating as the diamond
marks differently on the different parts of the plate.

These give illustrations of the results accomplished, but of course
many other experiments have been made. I have not yet been able to
decide whether the definition of the concave grating fully comes up to
that of a fiat grating, but it evidently does so very nearly.

ON- CONCAVE GRATINGS FOE OPTICAL PURPOSES"

[American Journal of Science [8], XXYI, 87-98, 1888; Philoeophical 3fagazine
[5], XVI, 197-SlO, 1888]

General Theory

Having recently completed a very successful machine for ruling
gratings, my attention naturally called to the effect of irregularity
in the form and position of the lines and the form of the surface on
the definition of the grating. Mr. C. S. Peirce has recently shown, in
the American Journal of Mathematics, that a periodic error in the
ruling produces what have been called ghosts in the spectrum. At first
I attempted to calculate the effect of other irregularities by the ordi-
nary method of integration, but the results obtained were not commen-
surate with the labor. I then sought for a simpler method. Guided by
the fact that inverse methods in electrical distribution are simpler
than direct methods, I soon found an inverse method for use in this
problem.

In the use of the grating in most ordinary spectroscopes, the tele-
scopes are fixed together as nearly parallel as possible, and the grating
turned around a vertical axis to bring the different spectra into the
field of view. The rays striking on the grating are nearly parallel,
but for the sake of generality I shall assume that they radiate from a
point in space and shall investigate the proper ruling of the grating
to bring the rays back to the point from which they started. The wave
fronts mil be a series of spherical shells at equal distances apart. If

lAn abstract of this paper with some other matter was giyen at the Physical
Society of London in November last, the paper being in my hand in its present shape
at that time. As I wished to make some additions, for which I have not yet had
time, I did not then publish it. I was mnch surprised soon after to see an article
on this subject which had been presented to the Physical Society and was published
in the Philosophical Magazine. The article contains nothing more than an exten-
sion of my remarks at the Physical Society and formulae similar to those in this
paper. As I have not before this published anything except a preliminary notice of
the concave gratings, I expected a little time to work up the subject, seeing that the
practical work of photographing the spectrum has recently absorbed all my time.
But probably I have waited too long.

On Concave Gratings fob Optioai Purposes

493

these vaves strike or a reflecting surface, they will he reflected hack
provided they can do so all in the same phase. A sphere around the
radiant point satisfies the condition for waves of all lengths and thus
gives the ease of ordinary reflection. Let any surface cut the wave
surfaces in any manner and let us remove tlrose portions of the surface
which are cut hy the wave surfaces ; the light of that particular wave-
length can then he reflected hack along the same path in the same
phase and thus, hy the above principle, a portion will he sent hack.
But the solution holds for only one wave-length and so white light will
he drawn out into a spectrum. Hence we have the important conclu-
sion that a theoretically perfect grating for one position of the slit and
eye-piece can he ruled on any surface, flat or otherwise. This is an
extremely important practical conclusion and explains many facts which
have been observed in the use of gratings. For we see that errors of
the dividing engine can he counterbalanced hy errors in the flatness of
the plate, so that a had dividing engine may now and then make a
grating which is good in one spectrum but not in all. And so we often
find that one spectrum is better than another. Furthermore Professor
Young has observed that he could often improve the definition of a
grating by slightly bending the plate on which it was ruled.

From the above theorem we see that if a plate is ruled in circles
whose radius is r sin ft and whose distance apart is dr ! sinyM, where dr
is constant, then the ruling will he appropriate to bring the spectrum
to a focus at a distance, r, and angle of incidence, [jl. Thus we should
need no telescopes to view the spectrum in that particular position of
the grating. Had the wave surfaces been cylindrical instead of spher-
ical the lines wo\fld have been straight instead of circular, hut at the
above distances apart. In this case the spectrum would have been
brought to a focus, but would have been diffused in the direction of
the lines. In the same way we can conclude that in flat gratings any
departure from a straight line has the effect of causing the dust ih the
slit and the spectrum to have different foci, a fact sometimes observed.

We also see that, if the departure from equal spaces is small, or, in
other words, the distance r is groat, the lines must be ruled at distances
apart represented by

* + &o.)

\ r sin fi J

in order to bring the light to a focus at the angle // and distance r, c

being a constant and x the distance from some point on the plate.

fjL changes sign, then r must change in sign

Hence we see that the

494

Henkt a. Eowland

effect of a linear error in the spacing is to make the focus on one side
shorter and the other side longer than the normal amount. Professor
Peirce has measured some of Mr. Eutherfurd^s gratings and found that
the spaces increased in passing along the grating, and he also found
that the foci of symmetrical spectra were different. But this is the
first attempt to connect the two. The definition of a grating may
thus he very good even when the error of run of the screw is consider-
able, provided it is linear.

ConroAVE Geatings

Let us now take the special case of lines ruled on a spherical surface;
and let us not confine ourselves to light coming back to the same point,
but let the light return to another point. Let the co-ordinates of the
radiant point and focal point beyi=0, £c = — a and y = 0, a; + a, and
let the centre of the sphere whose radius is p be at y'. Let r be the
distance from the radiant point to the point a;, y, and let R be that from
the focal point to x, y. Let us then write

%’b = R -frc,

where c is equal to ± 1 according as the reflected or transmitted ray is
used. Should we increase b by equal quantities and draw the ellip-
soids or hyperboloids so indicated, we could use these surfaces in the
same way as the wave surfaces above. The intersections of these
surfaces with any other surface form what are known as Huyghens’
zones. By actually drawing these zones on the surface, we form a
grating which will diffract the light of a certain wave-length to the
given focal point. For the particular problem in hand, we need only
work in the plane x, y for the present.

Let s be an element of the curve of intersection of the given surface
with the plane x, y. Then our present problem is to find the width of
Huyghens^ zones on the surface, that is ds in terms of db.

The equation of the circle is

(a— =

and of the ellipse or hyperbola

R + rc = 2b

or (5“— a») af + by = 5* (b^—a^)

in which c has disappeared.

Ji/ + dy ^ ;

dx y -—y'

dy £C — jc' '

On Concave Geatings eos Optical Pubposes

495

disj CJ» — a*) x—Vy j. = J { 2J> — (a^' + + a'')\dl,

e^y I _ a: + Vy'^ = b{%}^ - (id + y' + a')\dl,

• - h 25* — fig* + y‘ + d)

' ‘ ’25’ ^ (6* — a^xy “V) ^ — ^) y *

This equation gives us the proper distance of the rulings on the sur-
face, and if we could get a dividing engine to rule according to this
formula the problem of bringing the spectrum to a focus without tele-
scopes would be solved. But an ordinary dividing engine rules equal
spaces and so we shall further investigate the question whether there
is any part of the circle where the spaces are equal. We can then write

And the differential of this with regard to an arc of the circle must
be zero. Differentiating and reducing by the equations

we have

di _ p

P j 2iB5(y—y) — 2y6 (*—«')— [65*— (aj* + y’ + a*)] |

+ (y— a*)(y— yO — (*—

+ ^[®(y-y)-yC*-*')]} = o.

It is more simple to express this result in terms of B, r, p and the
angles hetveen them.

Let p be the angle between p and r, and v that between p and B. Ijet
us also put

Let Y and S also represent the angles made by r, B and p respec-
tively with the line joining the source of light and focus, and let

Then we have

Bcoby + rctOB ^ sin j' -I- r sin jS . ^
2 ’ ^ 2"” ' ‘ ’

r cos — J? cos y
2

496

Hbney a. Rowland

(V — a^){y — y’f + J* (a; — o!y = (i* — a* sin* d ) ,

V -- ^ Rr cos* a ,

SITXT} =

R T
2a

sin a;

cos =

r-iZ

cos Of

= r = b + -jX,

^ = S52!J; y = a?iELiiE^

COS a ^ Sin a COS a

sini7 cos a,

J'y (y - y') + * (j’ - a*)(® - *') = ^ (cos + oos k) ,
35’ — (a* + y’ + a*) = Rr,

z (5* — a’)(y — y')—t‘y(x — a/)= (sin /i + sin v),

Sin /i + sin w oos a sin e

2a coBb = r COB ju — R cos v,

2a sin ^ = r sin ft-— R Bin v .

On substituting these values and reducing, we find

a _ 2 JZr cos a COB e

P — r cos*v + R cos* At ’

more simple solution is the following: must he constant in the direction

in which the diyiding engine rules. If the dividing engine rules in the direction of
the axis y, the differential of this with respect to y must he zero. But we can also
take the reciprocal of this quantity and so we can write for the equation of condi.
tion

d f?(JB + r) ^ Q
dy 5i

Taking a circle as our curve we can write

(» — ®/)s + CZ^ — y^f =

and (jc — + (y — = J?9,

{X ZWJS + (y y///)8 =:

T { - "-’i^ * '-=^) f

d d{B ■¥ v) _ 1 (X — ^ X —

- - +—

Making
we have

-ajw

’IT

■(V

-VO p

— a;'')(y — y'^)

— w

+ <J‘ — v"O^V—v"0 ~^ __

r»

: 0 .

it = 0, tf=0, v' = 0, */=p,

x" , xff^ f *''9 , a!W9\

^ + ___p(^^ + ^)=0,

n“Br + c osv _ SjRr cos a cos g

r cos* V + JB cos* u. rco8*v + ^008*^* *

On Oonoate Geatings eob Optical Pxtbposbs

497

Whence the focal length is

pR OOS*;tt

“ 'ZR cos a cos e — p COS* v '

For the transmitted beam, change the sign of B. Supposing p, B and v
to remain constant and r and p to vary, this equation will then give the
line on which all the spectra and the central image are brought to a
focus.

By far the most interesting case is obtained by making
r= pQQBfi, B = p OOBv,

since these values satisfy the equation. The line of foci is then a
circle with a radius equal to one-half p. Hence if a source of light

exists on this circle, the reflected image and all the spectra will be
brought to a focus on the same circle. Thus if we attach the slit, the
eye-piece and the grating to the three radii of the circle, however we
move them, we shall always have some spectrum in the focus of the
eye-piece. But in some positions the line of foci is so oblique to the
direction of the light that only one line of the spectrum can be seen
well at any one time. The best position of the eye-piece as far as we
consider this fact is thus the one opposite to the grating and at its
centre of curvature. In this position the line of foci is perpendicular
to the direction of the light, and we shall show presently that the
spectrum is normal at this point whatever the position of the slit, pro-
vided it is on the circle.

Eig. 1' represents this case; A is the slit, 0 is the eye-piece, and B is
the grating with its centre of curvature at 0. In this case all the con-
ditions are satisfied by fixing the grating and eye-piece to the bar BO
82

498

Henry A. Eowland

whose ends rest on carriages moving on the rails AB and A (7 at right
angles to each other; when desired, the radius AD may he put in to hold
everything steady, but this has been found practically unnecessary.

The proper formulae for this case are as follows: If A is the wave-
length and w the distance apart of the lines of the grating from centre
to centre, then we have

1 _ ^ _ sin V
"CT ”” ■” 2 ’

where N is the order of the spectrum.

••• •

Now in the given case p is constant and so NA is proportional to the
line AG,. Or, for any .given spectrum, the wave-length is proportional
to that line.

If a micrometer is fixed at G we can consider the case as follows :

dfi

If D is the distance the cross-hairs of the micrometer move forward
for one division of the head, we can write for the point 0

and for the same point p is zero. Hence

But this is independent of p and we thus arrive at the important fact
that the value of a division of the micrometer is always the same for
the same spectrum and can always be determined with sufficient accu-
racy from the dimensions of the apparatus and number of lines on the
grating, as well as by observation of the spectrum.

Purthermore, this proves that the spectrum is normal at this point
and to the same scale in the same spectrum. Hence we have only to
photograph the spectrum to obtain the normal spectrum and a centi-
meter for any of the photographs always represents the same increase
of wave-length.

It is to be specially noted that this theorem is rigidly true whether
the adjustments are correct or not, provided only that the micrometer
is on the line drawn perpendicularly from the centre of the grating, even
if it is not the centre of curvature.

On Concave Gratings for Optical Purposes

499

As the radius of curvature of concave gratings is usually great, the
distance through which the spectrum remains practically normal is very
great. In the instrument which I principally use, the radius of curva-
ture p, is about 21 feet 4 inches, the width of the ruling being about 6-6
inches. In such an instmment the spectrum thrown on a flat plate is
normal within about 1 part in 1,000,000, for 6 inches and less than 1 in
35,000, for 18 inches. In photographing the spectrum on a flat plate,
the deflnition is excellent for 12 inches, and by use of a plate bent to 11
feet radius, a plate of 20 inches in length is in perfect focus and the
spectrum still so nearly normal as to have its error neglected for most
purposes.

Another important property of the concave grating is that all the
superimposed spectra are in focus at the same point, and so by micro-
metric measurements the relative wave-lengths are readily determined.
Hence, knowing the absolute wave-length of one line, the whole spec-
trum can be measured. Professor Peirce has determined the absolute
wave-length of one line with great care and I am now measuring the
coincidences. This method is greatly more accurate than any hitherto
known, as by a mere eye inspection, the relative wave-length can often
be judged to 1 part in 20,000 and with a micrometer to 1 in 1,000,000.
Again, .in dealing with the invisible portion of the spectrum, the focus
can be obtained by examining the superimposed spectrum. Oaptain
Abney, by using a concave mirror in the place of telescopes, has been
enabled to use this method for obtaining the focus in photographing the
ultra red rays of the spectrum. It is also to be noted that this theorem
of the normal spectrum applies also to the flat grating used with tele-
scopes and to either reflecting or transmitting gratings; but in these
cases only a small portion of the spectrum can be used, as no lens can
be made perfectly achromatic. And so, as the distance of the microme-
ter has constantly to be changed when one passes along the spectrum,
its constant does not remain constant but varies in an irregular man-
ner. But it would be possible to fix the grating, one objective and the
camera rigidly on a bar, and then focus by moving the slit or the other
objective. In this case the spectrum would be rigidly normal, but
would probably be in focus for only a small length and the adjustment
of the focus would not be automatic.

But nothing can exceed the beauty and simplicity of the concave gra'f-
ing when mounted on a movable bar such as I have described and illus-
trated in Fig. 1. Having selected the grating which we wish to use,
we mount it in its plate-holder and put the proper collimating eye-piece

600

Henbt a. EOWtAND

in place. We then carefully adjust the focus by altering the length of
B nutil the cross-hairs are at the exact centre of curvature of the grat-
ing. On moving the bar the whole series of spectra are then in exact
focus, and the value of a division of the micrometer is a known quan-
tity for that particular grating. The wooden way AC, on which the
carriage moves, is graduated to equal divisions representing wave-
lengths, since the wave-length is proportional to the distance AO. Wc
can thus set the instrument to any particular wave-length we may wish
to study, or even determine the wave-length to at least one part in five
thousand by a simple reading. By having a variety of scales, one for
apectrum, we can immediately see what lines are superimposed on
each other and identify them accordingly when we are measuring their
relative wave-length- On now replacing the eye-piece by a camera, we
are in a position to photograph the spectrum with the greatest ease.
We put m the sensitive plate, either wet or dry, and move to the part
we wish to photograph; having exposed for that part, we move to
another part, raise the plate to another position and expose once more.
We have no thought for the focus, for that remains perfect, but simply
refer to the table giving the proper exposure for that portion of the
spectrum and so have a perfect plate. Thus we can photo^ph the
whole spectrum on one plate in a few minutes, from the F line to the
extreme violet in several strips, each 20 inches long. Or we may photo-
graph to the red rays by prolonged exposure. Thus the work of days
with any other apparatus becomes the work of hours with this. Fur-
thermore, each plate is to scale, an inch on any one of the strips repre-
senting so much diSerence of wave-length. The scale of the

different orders of spectra are exactly proportional to the order. Of
course the superposition of the spectra gives the relative wave-length.
To get the superposition, of course, photography is the best method.

Having so far obtained only the first approximation to the theory of
the concave grating, let us now proceed to a second one. The dividing
engine rules equal spaces along the chord of the circular arc of the grat-
ing: the question is whether any other kind of ruling would be better,
for the dividing engine is so constructed that one might readily change
it to rule slightly different from' equal spaces.

The condition for theoretical perfection is that 0 shall remain con-
stant for aU portions of the mirror. I shall therefore investigate how
nearly this is true.

Let p be the radius of curvature and let 1? and r be the true dis-
tances to any point of the grating, Bo and ro being the distances to the

On Concave Geatings pok Optical Pueposes

601

centre. Let /£ and p be the general valnes of the angles and /iq and
the angles referred to the centre of the mirror. The condition is that

^ = sm /jt 4- sin v

shall be a constant for all parts of the surface of the grating. Let us
then develops sin fi and sin v in terms of Vq and the angle 8 between
the radii drawn to the centre of the grating and to the point under con-
sideration. Let S be the angle between B and Bo- Then we can write
immediately

sin = /> sin mo cos ^ -1- sin 5' — ^ cos /£« siJi ^9

sin M = sin aiq cos / 1+ a tan 1,

I /?smA4, P

where — 1 P cos /jIo

Developing the value of cos d' in terms of d, we have
cos = cos d 1 1 + 1 ^ 14 . d

~ ■^)] ^ }•
As the cases we are to consider are those where A is small, it will he
sufficient to write

tan 3' = tf .

’Whence we have

sin ti = sin /x, cos « 1 1 + aatii^AS + -^[^1+ ^ ^ ^

+ (a+-|.))] ^+4., }

’We can write the value of sin v from symmetry. But we have

a -^ = sin /I + sin v .

In this formula, can he considered as a constant depending on the
wave-length of light, etc., and ds as the width apart of the lines on the
grating. . The dividing engine rules lines on the curved surface accord-
ing to the formula

2 -^ = 008^ (sin Mt+ sin v,).

But this is the second approximation to the true theoretical ruling.
And this ruling will not only he approximately correct, hut exact when

608

Henry A. Eowland

all tiie teraiB of the series except the first vanish. In the case where the
sUt and focus are on the circle of radius y, as in the automatic arrange-
ment described above, we have A = 0 and the second and. third terms of
the series disappear, and we can write since we have

= cos
p

cos S (sin //o+ sinvo

and = cosv,,

1 sin ^11 tan mo + *'» -l. Ac,

’ sin /Jt + sin v.

But in the automatic arrangement we also have V(, — 0, and so the
formula becomes

2 = cos IS (sin //, +• sin

. ds

To find the greatest departure from theoretical perfection, d must
refer to the edge of the grating. In the gratings which I am now mak-
ing, jO is about 260 inches and the width of the grating about 5-4 inches.

Hence d = approximately and the series becomes

1 -

2,000,000

tan tJ„ .

Hence the greaiest departure from the theoretical ruling, oven when
tan;Utf:T= 2, is 1 in 1,000,000. How the distance apart of the compon-
ents of the 147'4 line is somewhat nearly one forty-thousandth of the
wave-length and I scarcely suppose that any line has been divided by
the beet spectroscope in the world whose components are less than onc-
third of this distance apart. Hence we see that the departure of the
ruling from theoretical .perfection is of little consequence until we are
able to divide lines twenty times as fine as the 1474 line. Even in that
case, since the error of ruling varies as d* , the greater portion of the
grating would be ruled correctly.

The question now comes up as to whether there is any limit to the
resolving power of a spectroscope. This evidently depends upon the
magnifying power and the apparent width of the lines. The magnify-
ing power can be varied at pleasure and so wo have only to consider the
width of the lines of the spectrum. The width of the linos evidently
depends, in a perfect grating, upon three circumstances, the width of
the slit, the number of lines in the grating and the true physical width
of the line. The width of the slit can be varied at pleasure, the number
of lines on the grating can be made very great (160,000 in one of mine),
and hence we are only limited by the true physical width of the lines.

On Concave Gratinos for Optical Purposes

503

We have mimerous cases of wide lines, such, as the G line, the compon-
ents of tile D * and H lines and minicrona others which are perfectly
familiar to every spectroseopist. Hence we are free to suppose that all
lines have some physical width, and we are limited by that width in the
resolving power of our spectroscope. Indeed, from a theoretical stand-
point, we should suppose this to be true : for the molecules only vibrate
freely while swinging through their free path and in order to have the
physical width one one-hundrcd-tliousandth of the wave-length, the
molecule must make somewhat nearly one hundred thousand vibrations
in its free patli: but this would require a free path of about
inch! Hence it would be only the outermost solar atmosphere that could
produce such fine lines and we could hardly expect to see much finer
ones in the solar spectrum. Again* it is found impossible to obtain
interference between two rays whose paths differ by much more than
e50,000 wave-lengths.

All the methods of determining the limits seem to point to about the
160,000th of tlie wave-length as the smallest distance at which the two
lines can be separated in the solar spectrum by even a spectroscope of
infinite power. As we can now nearly approach this limit I am strongly
of the opinion, that we have nearly reached the limit of resolving power,
and that we can never hope to see very many more lines in the spectrdm
than can be seen at present, either by means of prisms or gratings.

It is not to be supposed, however, that the average wave-length of the
line is not more definite than this, for we can easily point the cross-
hairs to the centre of the line to perhaps 1 in 1,000,000 of the wave-
length. The most exact method of detecting the coincidences of a line
of metal with one in the solar spectrum would thus be to take micro-
metric measurements first on one and then on the other; but I suppose
it would take several readings to make the determination to 1 in
1,000,000.

Since writing the above I have greatly improved my apparatus and
can now photograph 150 lines between the H and K lines, including
many whose wave-length does not differ more than 1 in about 80,000.
I have also photographed the 1474 and and 64, widely double, and also
E just perceptibly double. With the eye much more can be seen, but
I must say that I have not yet seen many signs of reaching a limit. The

3 1 have recently discovered that each component of the D line is double probably
from the partial reversal of the line as we nearly always see it in the flame spectrum.

^ This method of determining the limit has been sugic^sted to me by Prof. C. S.
Hastlnjrs, of this University.

504:

Henry A. Eowland

lines yet appear as fLne and sharp as with a lower power. If my grat-
ing is asstuned to he perfect, in the third spectrum I should he able to
divide lines whose wave-lengths differed, in about 160,000, though not
to photograph them.

The JE line has components, about y y^ yth of the wave-length apart.
I believe I can resolve lines much closer than this> say 1 in 100,000 at
least. Hence the idea of a limit has not yet been proved.

However, as some of the lines of the spectrum are much wider than
others we should not expect any definite limit, but a gradual falling off
as we increase our power. At first, in the short wave-lengths at least,
the number of lines is nearly proportional to the resolving power, but
this law should fail as we approach the limit.

ON ME. GLAZEBEOOK'S PAPEE ON THE ABEEEATION OP
CONCAVE GEATINGS

[American Journal of Seietice [81, XXVI^ 214, 1888; Fhiloaophical Afagaaine [6],

Xri, 210, 1888]

In the June number of the Philoeophical Magazine, Mr. E. T. Glaze-
brook has considered the aberration of the concave grating and arrives
at the conclusion that the ones which I have hitherto made are too
wide for their radius of curvature. As I had published nothing but a
preliminary notice of the grating at that time, Mr. Glazebrook had not
then seen my paper on the subject, of which I gave an abstract at the
London Physical Society in November last. In this paper I arrive at
the conclusion that there is practically no aberration and that in this
respect there is nothing further to be desired.

The reason o-f this discrepancy is not far to seek. Mr. Glazebrook
assumes that the spaces are equal on the arc of the circle. But I do
not rule them in this manner; but the equal spaces are equal along
the chord of the arc. Again, the surface is not cylindrical, but spherical.

These two errors entirely destroy the value of the paper as far as my
gratings are concerned, for it only applies to a theoretical grating, ruled
in an entirely different manner from my own, and on a different form
of surface.

I am very much surprised to see the method given near the end of
the paper for constructing aplanatic gratings on any surface, for this
is the method by which I discovered the concave grating originally, and
the figure is the same as I jmt on the blackboard at the meeting of the
Physical Society in November last. I say I am surprised, for Mr. Glaze-
brook's paper was read at the Physical Society, where I had given the
same method a few months before, and yet it passed without comment.
Indeed, I have given the same method many times at various scientific
societies of my own country. However, as Mr. Glazebrook was not
present at the meeting referred to, he is entirely without blame in the
matter.

SCEEW

IMiuiyelopoidia Sriianntea, Ninth Nation, Yolumt XXI J

The screw is the simplest instrument for converting a uniform motion
of rotation into a uniform motion O’f translation (see ‘ Mechanics/ vol.
XT, p. 754). Metal screws requiring no special accuracy are generally cut
by taps and dies. A tap is a cylindrical piece of steel having a screw
on its exterior with sharp cutting edges; by forcing this with a revolv-
ing motion into a hole of the proper size, a screw is cut on its interior
forming what is known as a nut or female screw. The die is a nut with
sharp cutting edges used to screw upon the outside of round pieces of
metal and thus produce male screws. More accurate screws are cut in
a lathe by causing the carriage carrying the tool to move uniformly for-
ward, thus a continuous spiral line is cut on the uniformly revolving
cylinder fixed between the lathe centres. The cutting tool may be an
ordinary form of lathe tool or a revolving saw-like disk (see ‘ Machine
Tools,’ vol. XV, p. 153).

Errors of Screws . — ^For scientific purposes the screw must be so regu-
lar that it moves forward in its nut exactly the same distance for each
given angular rotation around its axis. As the mountings of a screw
introduce many errors, the final and exact test of its accuracy can only
be made when it is finished and set up for use. A large screw can, how-
ever, be roughly examined in the following manner: (1) See whether
the surface of the threads has a perfect polish. The more it departs
from this, and approaches the rough, tom surface as cut by the lathe
tool, the worse it is. A perfect screw has a perfect polish. (2) Mount
upon it between the centres of a lathe and the slip a short nut which
fits perfectly. If the nut moves from end to end with equal friction,
the screw is uniform in diameter. If the nut is long, rinequal resist-
ance may be due to either an error of run or a bond in the screw.
(3) Fix a microscope on the lathe carriage and focus its single cross-
hair on the edge of the screw and parallel to its axis. If the screw runs
true at every point, its axis is straight. (4) Observe whether the short
nut runs from end to end of the screw without a wabbling motion wli'*n
the screw is turned and the nut kept from revolving. If it wabbles the

SOKEW

-507

screw is said to te drunk. One can see this, error better by fixing a
long pointer to the nut, or by attaching to it a mirror and observing an
image in it with a telescope. The following experiment will also detect
error: (5) Put upon the screw two well-fitting and rather short
mits, which are kept from revolving by arms bearing against a straight
edge parallel to the axis of the screw. Let one nut carry an arm which
supports a microscope focused on a line ruled on the other nut. Screw
this combination to different parts of the screw. If during one revolu-
tion the microscope remains in focus, the screw is not drunk; and if
the cross-hairs bisect the lines in every position, there is no error of
run.

Making Accurate Screws . — ^To produce a screw of a foot or even a
yard long with errors not exceeding T 5 *inrth of an inch is not difficult.
Prof. Wm. A. Eogers, of Harvard Observatory, has invented a process
in which the tool of the lathe while cutting the screw is moved so as to
counteract the errors of the lathe screw. The screw is then partly
ground to get rid of local errors. But, where the highest accuracy is
needed, we must resort in the case of screws, as in all other cases, to
grinding. A long, solid nut, tightly fitting the screw in one position,
cannot be moved freely to another position unless the screw is very accu-
rate. If grinding material is applied and the nut is constantly tight-
ened, it will grind out all errors of run, drunkenness, crookedness, and
irregularity of size. The condition is that the nut must be long, rigid
and capable of being tightened as the grinding proceeds ; also the screw
must be ground longer than it will finally be needed so that the imper-
fect ends may be removed.

The following process will produce a screw suitable for ruling grat-
ings for optical puri;)ose8. Sxxpposc it is our purpose to produce a screw
which is finally to bo 9 inches long, not including bearings, and in-
in diameter. Select a bar of soft Bessemer steel, which has not the
hard spots usually found in east steel, and about Ift inches in diameter;
and 30 long. Put it between lathe centres and turn it down' to one
inch diameter everywhere, except about 19 inches in the centre, where
it is left a little over inches in diameter for cutting the screw. How
cut the screw with a triangular thread a little sharper than CO . Above
all, avoid a fine screw, using about SO threads to the inch.

The grinding nut, about 11 inches long, has now to bo made. Pig. 1
represents a section of the nut, which is made of brass, or better, of
Bessemer steel. It consists of four segments, — o, a, which can be drawn
about the screw by two collars, 6, 6, and the screw c. Wedges between

508

Henet a. Rowland

the segments prevent too great pressure on the screw. The final damp-
ing is effected hy the rings and screws, d, d, which enclose the flanges, a,
of the segments. The screw is now placed in a lathe and surrounded
by water whose temperature can be kept constant to 1® 0., and the nut
placed on it. In order that the weight of the nut may not make the
ends too small, it must either be counterbalanced by weights hung from
a rope passing over pulleys in the ceiling, or the screw must be vertical
during the whole process. Emery and oil seem to be the only available
grinding materials, though a softer silica powder might be used towards
the end of the operation to clean off the emery and prevent future wear.
Now grind the screw in the nut, making the nut pass backwards and
forwards over the screw, its whole range being nearly 20 inches at first.

d d

Turn the nut end for end every ten minutes and continue for two weeks,
finally making the range of the nut only about 10 inches, using finer
washed emery and moving the lathe slower to avoid heating. Finish
with a fine silica powder or rouge. During the process, if the thread
becomes too blunt, recut the nut by a short tap so as not to change the
pitch at any point. This must, of course, not be done loss than five
days before the finish. Now cut to the proper length; centre again in
the lathe under a microscope, and turn the bearings. A screw so ground
has less errors than from any other system of mounting. The periodic
error especially will be too small to be discovered, though the mountings
and graduation and centering of the head will introduce it; it must
therefore finally be corrected.

Mounting of Screws . — The mounting must be devised most carefully,
and is, indeed, more difiSeult to make without error than the screw itself.
The principle which should be adopted is that no workmanship is per-
fect; the design must make up for its imperfections. Thus the screw

SOBEW

609

can. never be made to run true on its bearings, and bence the device of
resting one end of the carriage on the nut must be rejected. Also all
rigid connection between the nut and the carriage must be avoided, as
the screw can never be adjusted parallel to the ways on which the car^
riage rests. For many purposes, such as ruling optical gratings, the
carriage must move accurately forward in a straight line as far as the
horizontal plane is concerned, wMle a little curvature in the vertical
plane produces very little effect. These conditions can be satisfied
by making the ways V-shaped and grinding witih a grinder some-
what shorter th an tte ways. By constant reversals and by lengthen-
ing or shortening the stroke, they will finally become nearly per-
fect. The vertical curvature can be sufficiently tested by a short car-
riage carrying a delicate spirit level. Another and very efficient form
of ways is V-shaped with a fiat top and nearly vertical sides. The
carriage rests on the flat top and is held by springs against one of -the
nearly vertical sides. To determine with accuracy whether the ways
are siraight, fix a flat piece of glass on the carriage and rule a line on
it by moving it under a diamond; reverse and rule another line near the
first, and measure the distance apart at the centre and at the two ends
by a micrometer. If the centre measurement is equal to the mean of the
two end ones, the line is straight. This is better than the method with
a mirror mounted on the carriage and a telescope. The screw itself
must rest in bearings, and the end motion be prevented by a point bear-
ing against its flat end, which is protected by hardened steel or a flat
diamond. Collar bearings introduce periodic errors. The secret of
success is so to design the nut and its connections as to eliminate all
adjustments of the screw and indeed all imperfect workmanship. The
connection must also be such as to give means of correcting any residual
periodic errors or errors of run which may be introduced in the mount-
ings or by the wear of the machine.

The nut is shown in Fig 2. It is made in two halves, of wrought iron
filled with boxwood or lignum vitae plugs, on which the screw is cut.
To each half a long piece of sheet steel is fixed which bears against a
guiding edge, to be described presently. The two halves are held to the
screw by springs, so that each moves forward almost independently of
the other. To join the nut to the carriage, a ring is attached to the
latter, whose plane is vertical and which can turn round a vertical axis.
The bars fixed midway on the two halves of the nut bear against this
ring at points 90° distant from its axis. Hence each half does its share
independently of the other in moving the carriage forward. Any want

510

Henby a. Rowland

of parallelism between the scjrews and the ways or eccentricity in the
screw mountings thus scarcely affects the forward motion of the car-
riage. The guide against which the steel pieces of the nut rest can be
made of such form as to correct any small error of run due to wear of
the screw. Also, by causing it to move backwards and forwards peri-
odically, the periodic error of the head and mountings can be corrected.

In making gratings for optical purposes the periodic error must be
very perfectly elinainated, since the periodic displacement of the lines
only one-millionth of an inch from their mean position will produce

Eia. 3. '

ghosts in the spectrum." Indeed, this is the most sensitive method of
detecting the existence of this error, and it is practically impossible to
mount the most perfect of screws without introducing it. A very prac-
tical method of determining this error is to rule a short grating with
very long lines on a piece of common thin plate glass; cut it in two with
a diamond and superimpose the two halves with the rulings together
and displaced sideways over each other one-half the pitch of the screw.
On now looking at the plates in a proper light so as to have the spec-

^ In a machine made by the present writer for rnling gratings the periodic error is
entirely due to the graduation and centering of the head. The uncorrected periodic
error from this cause displaces the lines ^-^j^p^th of an inch, which is sufficient to
entirely ruin all gratings made without correcting it.

SCEBW

511

tral colors show through it, dark lines will appear, which are wavy if
there is a periodic error and straight if there is none. By measuring
the comparative amplitude of the waves and the distance apart of the
two lines, the amount of the periodic error can he determined. The
phase of the periodic error is best found by a series of trials after set-
ting the corrector at the proper amplitude as determined above.

A machine properly made as above and kept at a constant tempera-
ture should be able to make a scale of 6 inches in length, with errors at
no point exceeding of an inch. When, however, a grating of

that length is attempted at the rate of 14,000 lines to the inch, four days
and nights are required, and the result is seldom perfect, possibly on
account of the wear of the machine or changes of temperature. Grat-
ings, however, less than 3 inches long are easy to make.

ON THE EELATIYE WAVE-LENGTH OP THE LINES OP THE

SOLAE SPECTETJM

lAmeHcim Journal of Sdsnce [8], XXXXII^ 183-190, 1887 ; Fhiloiophieal Magazine
[5], XXill, 357-266, 1887]

For several years past I have been engaged in making a photographic
map of the solar spectrum to replace the ordinary engraved maps and
I have now finished the map from the extreme ultra violet, wave-length
3200, down to- wave-length 6790. In order to place the scale correctly
on this map, I have found it necessary to measure the relative wave-
lengths of the spectrum and to reduce it to absolute wave-lengths by
some more modem determination. I have not yet entirely finished the
work, but as my map of the spectrum is now being published and as
aU observers so far seem to accept the measures of Angstroni, I have
decided that a table of my results would be of value. For as they stand
now they have at least ten times the accuracy of any other determina-
tion. This great accuracy arises from the use of the concave grating
which reduces the problem of relative wave-lengths to the measure of
the coincidences of the lines in the different spectra by a micrometer.

The instrument which I have employed has concave gratings 6 or 6 in.
diameter, having either 7200 or 14,400 lines to the inch and a radius of
21 ft. 6 in. By my method of mounting, the spectrum is normal where
measured, and thus it is possible to use a micrometer with a range of
5 inches. The spectrum keeps in focus everywhere and the constant
of the micrometer remains unchanged except for slight variations due
to imperfections in the workmanship. The micrometer has no errors
of run or period exceeding the o ii^ch. The probable error of a
single setting on a good clear line is about - go o^ TTTr wave-length.

1" of arc is about *0012 inch. The B line in the second spectrum is -17
inch or 4*4 mm. wide. Determinations of relative wave-length of good
lines seldom differ 1 in 600,000 from each other and never exceed 1 in
100,000, even with different gratings. This is, of course, for the prin-
cipal standard lines, and the chance of error is greater at the extremities
of the spectrum. The interpolation of lines was made by running the
micrometer over the whole spectrum, 6 inches at a time, and adding the

RbiiAtivb "Wave-Length gf Lines op Solar Speotrhm: 513

readings together so as to include any distance, oven the whole spec-
trum. The wave-length is calculated for a fixed micrometer constant
and then corrected so as to coincide everywhere very nearly with the
standards. I suppose the probable error of the relative determinations
with the weight 1 in my table to be not far from 1 in 600,000. Ang-
strSm thinks his standard lines have an accuracy of about 1 in 60,000
and ordinary lines much less.

As to the absolute measure, it is now well determined that AngstrSm’s
figures are too small by about 1 part in 6000. This rests: Ist, on the
determination of Peirce made for the "CJ. S. Coast Survey with Euther-
furd’s gratings and not yet completely published; 2d, on an error made
by Tresca in the length of the standard metre used by Angstrom * which
increases his value by about 1 in 7700; 3d, on 'a result obtained in my
laboratory with two of my gratings by Mr. Bell, which is published with
this paper. Mr. C. S. Peirce has kindly placed his grating at our dis-
posal and we have detected an error of ruling which affects his result
and makes it nearly coincide with our own. The wave-length of the
mean of the two B lines is

AngstrSm (atlas) 6269 '12 ± *6

Angstrfim (Corrected by Thal6n) 6269-80*

Peirce 6270-16

Peirce (Corrected by Rowland and Bell) 6270-00*

Bell 6270-04

These results aro for air at ordinary pressures and temperatures. The
last is reduced to 20° C. and 760 mm. pressure. To reduce to a vacuum
4 multiply by the following:

Fraunhofer lino A 0 . E Q H

Correction factor. .1-000291 1-000292 1 000294 1-000297 1-000298

The relation between my wave-lengths and those of AngstrBm are
given by the following, Angstrom’s value being from p. 31 of his

memoir:

, A (edge) n (odge) 0

AngstrSm 7697-6 6867-10 6717-16 6662-10 6264-81

Rowland 7693-97 6867-38 6717-83 6662-96 6266-27

Difference — 3-6 -28 -67 -86 ^

> Thslta, Bur Spectre da Per, Socidtd Royale dee Solenoet d’Upsal, September,
tSH4, p. SR. ‘From one grating only.

614

Hbnuy a. Bowland

Angstrom

Bowland

5896-13

6896-08

6889- 13

6890- 13

5708-46

6709-66

Felroe '8 line

6633-36

5634-70

6464-84

6466-68

Difference .....

-95

1-00

1-11

1-34

•84

Angstrom

Bowland

6369-59

5370-43

J5J

6368- 67

6369- 65

5183-10

5183-73

5138-78

6139-47

4860- 74

4861- 43

Difference

-84

-98

•63

•69

Angstrom

Bowland

4703-44

4703-11

4307-36

4307-96

Difference

' -67

-71

The greatest variation in these differences is evidently due to the
poor definition of Angstrom^s grating hy which the numbers refer to
groups of lines rather than to single ones. Selecting the best figures,
we find that Angstrom^s wave-lengths must be multiplied by 1*00016 to
agree with BeU, wMle the correction for Angstrom^s error of scale
would be 1 * 000110 .

It is impossible for me to give at present all the data on which my
determinations rest, but I have given in Table I many of the coinci-
dences as observed with several gratings, the number of single readings
being given in the parenthesis over each set.

Table 11 gives Ihe wave-lengths as interpolated by the micrometer,
it is scarcely possible that any error will be found (except accidental
errors) of more than * 02 , and from the agreement of the observations
I scarcely expect to make any changes in the final table of more than
- 01 , except in the extremities of the spectrum, where it may amount
to *03 in the region of A and JET lines. The wave-lengths of weight
greater than 1 will probably be found more exact than this. The lines
can be identified on my new photograph of the spectrum down to 6790.
Below this there k little trouble in finding the right ones. All maps
of the spectrum, especially above JF, are so imperfect that it is almost
impossible to identify my liaes upon them. The lines can only be prop-
erly identified by a power sufficient to clearly divide 63 and Some of
them are double and most of these have been marked, but as the table
has been made for my own use, I have not been very careful to examine
each line. This will, however, be finally done. Micrometric measures

Eblativh Wave-Length oe Lines of Solas Spbotrum 616

have now been made of nearly all the lines below 6 with a view of mak-
ing a map of this region.

Table I gives the coincidences of the different orders of the spectra
as observed vrith several concave gratings on both aides of the normal,
the numbers in the brackets indicating the number of observations. The
observations have been reduced as nearly as possible to what I consider
the true wave-length, the small difference from the numbers given in
Table II being the variation of the observations from the mean value.
The true way of reducing these observations would be to form a linear
equation for each series and reduce by the method of least squares. A
simpler way was, however, used and the relative wave-length of the
standard lines, marked 8 in Table II, was obtained; however, some
other observations were also included.

Table II gives the .wave-lengths reduced to Bell's value for the abso-
lute wave-length of the D line. These were obtained by micrometric
measurement from the standards as described before. The weights
are given in the first column and some of the lines, which were meas-
ured double, have also been marked. But the series has not yet been
carefully examined for doubles.

The method is so much more accurate than by means of angular
measurement that the latter has little or no weight in comparison.

This table is to be used in connection with my photographic map, of
the normal spectrum to determine the error of the latter at any point.
The map was^made by placing the photograph in contact with the scale,
which was the same for each order of spectrum, and enlarging the two
together. In this way the map has no local irregularities, although the
scale may be displaced slightly from its true position, and may be a little
too long or short, although as far as I have tested it, it seems to have
very little error of the latter sort. The scale was meant in all cases,
except the ultra violet, to apply to Peirce's absolute value and so the
correction is generally negative, as follows:

Approodmate correction to the photographic map of the normal spectrum to
reduce to latest absolute value.

strip 3300 to 3330

« 3376 to 3530

—05

•()(}

“ 3475 to 3730

—.-02

« 3676 to 3930

-10

“ 3876 to 4130

“ 4075 to 4330

—04

516

Henby a. SowiiAND

Strip 4275 to 4530.
“ 4480 to 4735
« 4685 to 4940
« 4875 to 5130

« 5075 to 5830
» 5215 to 5595

« 6415 to 6795

« 3710 to 3910
“ 3810 to 4000

Correction

about...

about..

-•08
— 10
—•18
—14
—16
—06
—04
—•20
—•14

It is to be' noted that the third spectrum of the map runs into the
second, so that it must not be used beyond -waye-length 3200, as it is
mised with the second in that region.

[The tables are omitted.]

TABLE OF STAITDARD WAVE-LENGTHS

Wohm Bopklm University CircularSy No. 78, p, 69, 1889 ; JPhiloBcphioal Magaxim [6],

XXVII, 479-484, 1889]

In the ^ American Journal of Science^ for March, 1887, and the ^ Lon-
don, Dublin and Edinburgh Philosophical Magazine^ for the same
month, I have published a preliminary list of standards as far as could
be observed with the eye, with a few imperfectly observed by photog-
raphy, the whole being reduced to BelFs and Peirce^s values for absolute
wave-lengths. Mr. Bell has continued his measurements and found a
slightly greater value for the absolute wave-length of the 2? line, and I
have reduced my standards to the new values.

Nearly the whole list has been gone over again, especially at the ends
around the A line and in the ultra violet. The wave-lengths of the ultra
violet were obtained by photographiug the coincidence with the lower
wave-lengths, a method which gives them nearly equal weight with
those of the visible spectrum.

The full set of observations will be published hereafter, but the pres-
ent series of standards can be relied on for relative wave-lengths to -02
division of Angstrom in most cases, though it is possible some of them
may be out more than this amount, especially in the extreme red.

As to the absolute wave-length, no further change will be necessary,
provided spectroscopists can agree to use that of my table, as has been
done by many of them.

By the method of coincidences with the concave grating the wave-
lengths have been interwoven with each other throughout the whole
table so that no single figure could be changed without affecting many
others in entirely different portions of the spectrum. The principal dif-
ference from the preliminary table is in the reduction to the new abso-
lute wave-length by which the wave-lengths are about 1 in 80,000 larger
than the preliminary table. I hope this difference will not be felt by
those who hpe used the old table because measurements to less than
division of Angstrom are rare, the position of the lines of many metals
being unknown to a whole division of Angstrom. As the new map of
the spectrum has been made according to this new table, I see no further
reason for changing the table in the future.

618

Hbnky a. Rowlan-d

No attempt has been made to reduce the figures to a vacuum as the
index of refraction of air is imperfectly known, but this should be done
where numerical relations of time period are desired.

In the column giving the weight, the primary standards are marked
8 and the other numbers give the number of separate determination of
the wave-length and thus, to some extent, the weight.

Many of these standards are double lines and some of them have
faint components near them, which makes the accuracy of setting
smaller. This is specially the case when this component is an
atmospheric line whose intensity changes with the altitude of the sun.
The principal doubles are marked with d, but the examination has not
been completed yet, especially at the red end of the spectrum.

[A table of the standard wave-lengths is given on p. 78 J. H. TJ. Oirc.,
but is o-mitted in this volume.]

A FEW NOTES ON THE USE OF GBATINQS

[JolvM JECopkins University Oireulars^ No. 78, pp. 78, 74, 1880]

The ghosts are very Treak in most of my gratings. They are scarcely
visible in the lower orders of spectra, but increase in intensity as com-
pared with the principal line as the square of the order of the spectrum.
Hence, to avoid them, obtain magnification by increasing the focal dis-
tances instead of going to the higher orders. The distances from the
principal line in my gratings are the same as the distances of the spectra
from the image of the slit when using a grating of 20 lines to the inch.
They are always symmetrical on the two sides, and about inch for
the violet and i inch for the red in a grating of 21 ft. 6 in. radius in all
orders of spectra. When the given line has the proper exposure on the
photographic plate, the ghosts will not show, but over-exposure brings
them out faintly in the third spectrum of a 20,000 grating or the 6th of
a 10,000 one. They never cause any trouble, as they are easily recog-
nized and never appear in the solar spectrum. In some cases the higher
orders of ghosts are quite as apparent as those of the first order.

The gratings with 10,000 lines to the inch often have better definition
than those of 20,000, as they take half the time to rule, and they are
quite as good for eye observation. They can also be used for photo-
graphing the spectrum Vy absorbing the overlying spectra, but there
are very few materials which let through the ultra violet and absorb the
longer wave-lengths. The 10,000 gratings have the advantage, how-
ever, in the measurement of wave-lengths by the overlapping spectra,
although this method is unnecessary since the completion of my map of
the spectrum. By far the best is to use a 20,000 grating and observe
down to the D line by photography, using erjthrosin plates from the F
line down to D. Below D, cyanine plates can be used, although the time
of exposure is from 10 to 60 minutes with a narrow slit. The solar
spectrum extends to wave-lengths 3000, and the map has been contin-
ued to this point. Beyond this, the coincidence with the solar spectrum
cannot be used, but those of the 1st and 2d or 2d and 3d spectra can be.

Some complaints have been made to me that one of my gratings has
no spectrum beyond 3400, even of the electric arc. I have never found
this the case, as the one I use gives w. 1. 2200, readily with 30 minutes
exposure on slow plates, requiring 6 minutes for the most sensitive

620

Hbnet a. Eowland

part and using the electric arc. With sensitive plates, the time can he
diminished to one-fifth of this.

For eye observations, a very low power eye-piece of 1 or 2 in. focus
is best. This, with a focus of 21 ft. 6 in. is equivalent to a plane grat-
ing with a telescope of a power of 100 or 200.

In measuring the spectra, an ordinary dividing engine with errors
not greater than bich can be used, going over the measurements
twice with the plate reversed between the separate series. The plates
are on so very large a scale that the microscope must have a very low
power. The one I use has a 1 inch objective and a 2 inch eye-piece.
The measured part of the plate is about a foot long, the plates being
19 in. long.

All the spectrum photographs taken at different times coincide per-
fectly, and this can be used for such problems as the determination of
the atmospheric lines. For this purpose, negatives at high and low
sun are compared by scraping the emulsion off from half the plates and
clamping them together with the edges of the spectra in coincidence.
The two spectra coincide exactly line for line except where the atmo-
spheric lines occur.

This method is specially valuable for picking out impurities in metal-
lic spectra, using some standard impurity in all the substances to give
a set of fiducial lines; or better, obtaining the coincidence of all the
metals with some one metal, such as iron. Making the iron spectrum
coincide on the two plates, the other spectra can be compared. This is
specially possible because the focus of a properly set up concave grating
need not be altered in years of use, for, when necessary, it can be ad-
justed at the slit, keeping the distance of the grating from the slit con-
stant.

The spectrum of the carbon poles is generally too complicated for
use with anything except the more pronounced lines of metals, there
being, at a rough guess, 10,000 lines in its spectrum. However, in pho-
tographing metallic spectra but few of these show on the plate, as they
are mostly faint. The spark discharge gives very nebulous lines for
the metals.

Most gratings are ruled bright in the higher orders, but this is more
or less difficult, as most diamond points give the first spectrum the
brightest. Indeed, it is very easy to obtain ruling which is immensely
bright in the first spectrum. Such gratings might be used for gaseous
spectra. Short focus gratings of 5 ft. radius of curvature, very bright
in the first order, require only a fraction of a second exposure for the
solar spectrum and the spectrum of a gas can be obtained in less than
an hour.

EEPORT OF PROGRESS IN SPECTRUM WORK.

[/oAn« Sofkint UnivtrtUy (Hrculart, No. SS, pp. 41, 48, 1891 ; AnurUxm Jownat of
Seimeo [8], XZ,X, 348, 244, 1891 ; The Ohemical Newt, LXIII, 188, 1891]

During the past year or two a great deal of work has "been done in
the photography of the spectra of elements and the identification of the
lines in the solar spectrum, which it will take a long time to work up,
ready for publication. Hence, I have thought that a short account of
what has been done up to the present time might be of interest to work-
ers in the subject. In the prosecution of the work financial assistance
has been received from the Rumf ord Fund of the American Academy of
Arts and Sciences, as well as from the fund given by Miss Bruce to the
Harvard Astronomical Observatory for the promotion of research in
astronomical physics, and the advanced state of the work is due to such
assistance.

The work may be summed up imder the following heads:

let. The spectra of all known elements, with the exception of a few
gaseous ones, or those too rare to be yet obtained, have been photo-
graphed in connection with the solar spectrum, from the extreme ultra
violet down to the D line, and eye observations have been made on many
to the limit of the solar spectrum.

2d. A measuring engine has been constructed with a screw to fit the
above photographs, which, being taken with the concave grating, are all
normal spectra and to- the same scale. This engine measures wave-
lengths direct, so that no multiplication is necessary, but only a slight
correction to get figures correct to of a division of Angstrdm.

3d. A table of standard wave-len^hs of the impurities in the car-
bons, extending to wave-length 2000, has been constructed to measura
wave-lengths beyond the limits of the solar spectrum.

4th. Maps of the spectra of some of the elements have been drawn
on a large scale ready for publication.

5th. The greater part of the lines in the map of the solar spectrum
have been identified and the substance producing them noted.

6th. The following rough table of the solar elements has been con-
structed entirely according to my own observations, although, of course,
most of them have been given by others.

522

Hhnbt a. EomiAND

I do not know which axe the new ones, hut call attention to Silicon,
Yanadinm, Scandixun, Yttrium, Zirconium, Glucinum, Germanium and
Erhium, as being possibly new.

Silicon has lines on my map at wave-lengths 3906-7, 4:103-1, 6708-7,
6772-3 and 6948-7. That at 3906-7 is the largest and most certain.
That at 4103-1 is also claimed by Manganese.

EJLBMENTS IN TTTHl SDN, AERANQBD ACCOEDING TO THE INTENSITY
AND THE NDllBEB OF LINES IN THE SOLAB SFECTBUM.

mo TO nraDNSiTT.

ACOOSniNG TO NUHBBB.

Calcium.

Iron (2000 or more).

Iron.

Nickel.

Hydrogen.

Titanium.

Sodium.

Manganese.

Hickel.

Chromium.

Magnesium.

Cobalt.

Carbon (200 or more).

Silicon.

Yanadium.

Almniniimn.

Zirconium.

Titanium.

Cerium.

Chromium.

Calcium (75 or more).

Manganese.

Scandium.

Strontium.

Neodymium.

Yanadium.

Lanthanum.

Barium.

Yttrium.

Carbon.

Niobium.

Scandium.

Molybdenum.

Yttrium.

Palladium.

Zirconium.

Magnesium (20 or more).

Molybdenum.

Sodium (11).

Lanthanum.

Silicon.

Niobium.

Strontium.

Palladium.

Barium.

Neodymium.

Aluminium (4).

Copper.

Cadmium.

Zinc.

Ehodium.

Cadmium.

Erbium.

Cerium.

Zinc.

Glucinum.

Copper (2).

Germanium.

Silver (2).

Eepobt ov Pbogbess nr Spbctexim Wobb:

Aocomuoro to intsksitt.
Ehodiuiu.

Silver.

Tin.

Lead.

Erbium.

Potassium.

AoooBnmo to minssB.
Glucinum (3).
Germanium.

Tin.

Lead (1).

Potassium (1).

DOUBTFUIi ELEMENTS.

Iridiiua.

Buthenium.

Tungsten.

Osiniiun.

Tantalum.

TJranium.

Platiaum.

Thorium.

AntimoBj.

NOT IN SOLAB SPEOTBXTM.

Caesium.

Bubidium.

Arsenic.

Gold.

Selenium.

Bismuth.

Indium.

Sulphur.

Boron.

Mercury.

Thallium.

Nitrogen (vacuum tube). Phosphorus.

Praeseodymium.

Bromine.

STTBSTAHOEB UOT TOft

Oxygen.

Holmium.

Chlorine.

Tellurium.

Thulium.

Iodine.

Gallium.

Terbium, etc.

Fluorine.

These tables

are to be accepted as preliminary

only, especially the

order in tbe first portion. However, being made with such a powerful
instrument, and with such care in the determination of impuritiesj, they
must still have a weight superior to most others published.

The substances under the head of ^^Hot in Solar Spectrum^' are
often placed there because the elements have few strong lines or none
at all in the limit of the solar spectrum when the arc spectrum, which
I have used, is employed. Thus boron has only two strong lines at 2497.
Again, the lines of bismuth, are all compound and so too diffuse to ap-
pear in the solar spectrum. Indeed, some good reason generally ap-
pears for their absence from the solar spectrum. Of course, this is
little evidence of their absence from the sun itself.

Indeed, were the whole earth heated to the temperature of the sun,
its spectrum would probably resemble that of the sun very closely.

Henry A. Eowland

With the high dispersion here used the ^T3asic lines^^ of Lockyer are
widely hroken up and cease to exist. Indeed^ it wonld be difficult to
prove anything except accidental coincidences among the lines of the
different elements. Accurate investigation generally reveals some slight
difference of wave-length or a common impurity.

furthermore, the strength of the lines in the solar spectrum is gen-
erally very nearly the same as that in the electric arc, with only a few
exceptions, as for instance calcium. The cases mentioned by Lockyer
are gtoerally those where he mistakes groups of lines for single lines
or even nodstakes the character of the line entirely. Altogether there
seems to be very little evidence of the breaking up of the elements in
the sun as far as my experiments go.

Even after comparing the solar spectrum with all known elements,
there are still many important lines not accounted for. Some of these
I have accounted for hy silicon and there are probably many more. Of
all known substances this is the most difficult to bring out the lines in
the visible spectrum although it has a jSne ultra-violet one. Possibly
iron may account for many more, and all the elements at a higher tem-
perature might develope more. Then, again, very rare elements like
scandium, vanadium, etc., when they have a strong spectrum, may cause
strong so-lar lines and thus we may look for new" and even rare elements
to account for very many more. Indeed, I find many lines accounted
for hy the rare elements in gadohnite, samarskite and f ergusonite other
than yttrium, erbium, scandium, praeseodymium, neodymium, lantha-
num and cerium, which I cannot identify yet and which may be without
a name, for this reason, and to discover rare elements, I intend jBbaally
to try u nkn own minerals, as my process gives me an easy method of
detecting any new substance or analyzing minerals however many ele-
ments they may contain.

The research is much indebted to the faithful and careful work of
Mr. L. E. Jewell who has acted as my assistant for several years.
Preliminary publications of results will be made in the 'University
Circulars.^

Among the lastest results I may mention the spectroscopic separation
of yttrium into three components, and the actual separation into two.

GEATINGS IN THBOEY AND PEACTICE'

[FhiloiephiGal Magazine [5], XXXY^ 897-419, 1898 ; Astronomy and Astro-Physics^

XII, 129-149, 1898]

Pabt I*

It is not my object to treat the theory of diffraction in general but
only to apply the simplest ordinary theory to gratinp made by ruling
grooves urith a diamond on glass or metal. This study I at ffrst made
with a view of guiding me in the construction of the dividing engine
for the manufacture of gratings, and I have given the present theory
for years in my lectures. As the subject is not generally understood
in all its bearings I have written it for publication.

Let p be the virtual distance redxujed to vacuo through which a ray
moves. Then the effect at any point wiE be found by the summation
of the quantity

A co8 5(p— Vt) + Esin J(p — Vt),
in which J = I being the wave-length. 7 is the velocity reduced to
vacuo, and t is the time. Making 0 = tan“’y we can write this

V A’ + jB* sin [<> + J Cp — 7i!)] .

The energy or intensity is proportional to (A® -(- E®).

Taking the expression

(A -l-iE)(r«(»-n)^

when i= its real part will be the previous expression for the

displacement.. Should we use the exponential expression instead of the
circular function in our summation we see that we can always obtain

1 1 am mnch inde'bted to Dr. Ames for looking over the proofs of this paper and
correcting some errors. In the paper I have, in order to make it complete, giren
some results obtained preyionsly by others, especially by Lord Bayleigh. The treat-
ment is, however, new, as well as many of the results. My object was originally to
obtain some guide to the eflect of errors in gratings so that in constructing my
dividing engine I might prevent their appearance if possible.

‘[Part II was never written.]

626

Hbnby a. Botnujo)

the intensity of the light hy multiplying the final result by itself with
— ♦ in place of + i, because we have

(A + — = A* + J5*,

In cases where a ray of light falls on a surface where it is broken
up, it is not necessary to take account of the change of phase at the
surface but only to sum up the displacement as given above.

In aU our problems let the grating be rather small compared with
the distance of the screen receiving the light so that the displacements
need not be divided into th^ components before summation.

Let the point a/, y', / be the source of light, and at the point », y, z
let it be broken up and at the same time pass from a medium of index
of refraction T to one of I. Consider the disturbance at a poiut zf','y",
z" in the new medium. It wiU be

where

= fl!"’ + y"* + + a? + _ 2 + yif' + zi /') ,

^ = a!'* + y'* + /> + a? + y* + — a (aa/ + + *«') .

Let ihe point a;, y, 2 be near the origin of co-ordinates as compared
trith a/, a' or x" , y", z" and let f and ^ be the direction

cosines of p and p. Then, writing

M = I' V*'’ + y'* + z!* + It/ of" + y"* + 2"*,

1 = Ja Fa',

ti = IP + /'/S',

V =Ir +!'■/,

we have, for the elementary displacement.

where

and

[JS — yi— Xaj—

' ^ Iiva;'’-h y'* +

Va/'>4-y"> +

r* = iS* y> + a*.

This equation applies to light in any direction. In the special case
of parallel light, for which * = 0, falling on a plane grating with’ lines
in the direction of z, one condition “will be that this expression must be
the same for all values of z.

Hence i/ = 0.

If is the order of the spectrum and a the grating space we shall
see further on that we also have the condition

2Tta

iajj. = 27ri\r=

Gratings in Thboet and Peaotiob

627

The diiectioD of the dijBEracted light will then be defined by the
equations

a'»+./9'» + /* =0,

1 y +iv'=o>

•whence

JV = i^a> + 2^JV/9-

PN*

J'y = -lr.

In the ordinary case where the incident and diffracted rays are per-
pendicular to the lines of the grating, we can simplify the equations
somewhat.

Let ip be tbe angle of incidence and ^ of dififraction as measured from
the positiTe direction of X.

A = 7' cos f + Jcos

JV = j» = /' sin ?> -I- 7 sin <&,

J =

where I is the ware-length in Tacuo.

In case of the reflecting grating I = T and we can write

^ = 7{C08^5 -l-cosV'}.

— - ilV’=A‘ = -^{sin <p + sin <l>\.

This is only a very elementary expression as the real value would
depend on the nature of the obstacle, the angles, etc., but it will be suffi-
cient for our purpose.

The disturbance due to any grating or similar body will then be very
nearly

where ds is a differential of the surface. For parallel rays, « = 0.

Plane Gratings

In this case the integration can often be neglected in the direction
of z and we can write for the disturbance in case of parallel rays,

g-ib(B-n) ds.

628

Henby a. Eowland

Case I. — Simple Periodic Bxjling

Let the surface be divided up into equal parts in each of which one
or more lines or grooves are ruled parallel to the axis of z.

The integration over the surface will then resolve itself into an
integration over one space and a summation with respect to the num-
ber of spaces. Por in this case we can replace ylayna + y where a is
the width of a space and the displacement becomes

but

n— 1 1 y w— sinw-^

Sin

ba/i

Multiplying the disturbance by itself wdth — i in place of we have
for the light intensity

sin n

sin

iapL

Tofi

The first term indicates spectral lines in positions givaa by the equation

sin^f = 0

■with intensities given hy the last .integral. The intensity of the spec-
tral lines then depends on the form of the groove aa given hy the equa-
tion x — f{y) and upon the angles of incidence and difEraction. The
first factor has been often discussed and it is only necessary to call
attention to a few of its properties.

When lafi<=Z7:N, N being any whole number, the expression be-
comes n®. On either side of this value the intensity decreases until
nbap!=:2TrN, when it becomes 0.

The spectral line then has a -width represented by// — //'= 2^ nearly;
on either side of this line smaller maxima exist too faintly to be ob-
served. When two spectral lines are nearer together than half their
width, they blend and form one line. The defining power of the spec-
troscope can be expressed in terms of the quotient of the wave-length
by the difference of wave-length of two lines that can just be seen as
dmded. The defining power is, then.

’n2r=m-!^

8 An expression of Lord Kayleigh’s.

Gbatistob in Theoby and Pbaotioe

5S9

Now ftffl is the width of the grating. Hence, using a grating at a
given angle, the defining power is independent of the number of lines
to the inch and only depends on the width of the grating and the wave-
length. According to this, the only object of ruling many lines to the
inch in a grating is to separate the spectra so that, with a given angle,
the order of spectrum, shall be less.

Practically the gratings with few lines to the inch are much better
than those with many, and hence have Mter defiboltion at a given
angle than the latter except that the spectra are more mixed up and
more difdcult to see.

It is also to be observed that the defining power increases with shorter
wave-lengths, so that it is three times as great in the ultra violet as
in the red of the spectrum. This is of course the same with all optical
instruments such as telescopes and naicroscopes.

The second term which determines the strength of the spectral lines
will, however, give us much that is new.

First let us study the effect of the shape of the groove on the bright-
ness. If N is the order of the spectrum and a the grating space we
have

fi = /(sin -I- sin </>) = ^
a

since sm-®^ = 0

and the intensity of the light becomes proportional to

It is to be noted that this expression is not only a function of N but
also of Zj, the wave-length. This shows that the intensity in general
may vary throughout the spectrum according to the wave-length and
that the sum of the light in any one spectrum is not always white light.

This is a peculiarity often noticed in gratings. Thus one spectrum
may be almost wanting in the green, while another may contain an
excess of this color; again there may be very little blue in one spectrum
while very often the similar spectrum on the other side may have its
own share and that of the other one also. For this reason I have found
it almost impossible to predict wliat the ultra red spectrum may be,
for it is often weak even where the visible spectrum is strong.

The integral may have almost any form although it will naturally
tend to be such as to make the lower orders the brightest when the
diamond rules a single and simple groove. When it rules several lines
34

630

Henky a. Eowland

or a compoimd groove, the higher orders may exceed the lower in
brightness and it is mathematically possible to have the grooves of
such a shape that, for given angles, all the light may be thrown into
one spectrum.

It is not uncommon, indeed, very easy, to rule gratings with im-
mensely bright jBrst spectra, and I have one grating where it seems as
if half the light were in the first spectrum on one side. In this case
there. is no reflection of any account from the grating held perpendicu-
larly: indeed to see one’s face, the plate must be held at an angle, in
which ease the various features of the face are seen reflected almost
as brightly as in a mirror but drawn out into spectra. In this case all
the other spectra and the central image itself are very weak.

. In general it would be easy to prove from the equation that want of
symmetry in the grooves produces want of synunetry in the spectra, a
fact universally observed in all gratings and one which I generally
utilize so that the light may be concentrated in a few spectra only.

Example 1. — Squaee Gbooves

When the light falls nearly perpendicularly on the plate, we need
not take the sides into account but only sum up the surface of the plate
and the bottom of the groove. Let the depth be X and the width equal

to£.

The intensity then becomes proportional to

sia’ w

sin* * -4- X.

This Tanishes when

N=m,

, 3m , etc..

=0,1,2, 3, etc.

The intensity O'f the central light, for -which iV' = 0, will be

This can be made to vanish for only one angle for a given wave-
length. Therefore, the central image will be colored and the color
will change with the angle, an effect often observed in actual gratings.
The color ought to change, also, on placing the grating in a liquid of
different index of refraction since A contains I, the index of refraction.

It will be instructive to take a special case, such as light falling per-
pendicularly on the plate. Eor this case

Gratings in Theort and Practice

631

= 0, A =7(1 + cos 4>) and /t = J sin

Hence A = jj 1 + ^1- }•

The last term in the intensity will then be

As an example, let the green of the second order vanish. In this case,
I = •00005. N = 2. Let a = -0003 cm. and 7 = 1.

Then, X[20000 -4- V (20000)* - (10000)*] = n .

Whence, ■p-_ n

* ~ 37300. ’

where n is any whole nmnber. Make it 1.

Then the intensity, as far as this term is concerned, will be as
follows:

Minima where Intensity is 0.
Wave-lengths.

Xst spec. -0000526 -0000268

2nd *0000500 *0000266

8rd -0000462 *0000263

4th -0000416 *0000259

5 th *« etc.

Maxima where Intensity is 1.
Wave-lengths.

•0001000 -00008544 -00002187

•0000888 -00008468 -00002119

•0000651 -00008888 -00002089

•0000499 -00008169 -00002060

etc. etc.

The central light will contain the following wave-lengths as a
maximum :

•0001072 -00003675 -0000214, etc.

Of course it would be impossible to find a diamond to rule a rectangu-
lar groove as above and the calculations can only be looked upon as a
specimen of innumerable light distributions according to tlio shape of
groove.

Every change in position of the diamond gives a different light dis-
tribution and hundreds of changes may be made every day and yet the
same distribution will never return, although one may try for years.

Example 2. — Tbiae-gulah Gboovb
Let the space a be cut into a triangular groove, the equations of the
sides being x = — cy, and x = c'{y — a), the two cuttings coming
together at the point y — u. Hence we have — cu = c'(u — a), and
ds = dy »/l+o^oT dy^l + d^. Hence the intensity is proportional to

532

Hbnet a. Bowlamt)

^ ^ ain* ^ 1 + c'* gjjji ’r(a — u)(ft-h</k)

^ + oTfTX)*

. V (1 + c*)(l + c^*) gjjj (^ — CA) Tc(ji— u)(/i + </ X
ili—Ot/Xfl + cfi.) i ' I

cos [(/i 4- c'A)(a — u) — n(ft — cA)]

}•

This expression is not symmetrical with respect to the normal to the
grating, unless the groove is symmetrical, in which case c==c' and

In this case, as in the other, the colors of the spectrum are of vari-
able intensity, and some of them may vanish as in the first example,
bnt the distribution of intensity is in other respects quite different.

Case IL — ^Multiple Pebiodio Ruling

Instead of having only one groove ruled on the plate in this space a,
let us now suppose that a series of similar lines are ruled.

We have, then, to obtain the displacement by the same expression as
before, that is

sin n

iapL

sin

3 r r

dfl/T J J

except that the last integral will extend over the whole number of lines
ruled within the space a.

In the spaces a let a number of equal grooves be ruled commencing
at the points y = 0, y %9 etc., and extending to the points 4" w,
ya 4- w, etc. The surface integral will then be divided into portions
from IV to from yj 4- w, to ya, etc., on the original surface of the
plate for which a; = 0, and from w to 0, from y^ + w to y^, etc., for
the grooves.

The first series of integrals will be

dy = -Hw) -|- — etc. }

= j — -f (1 — + gibMVa + etc.) +

But, — 1 since Ifjta = 2;riV' for any maximum, and thus the inte-
gral becomes

1 — f

ib/i

1 + + giftfiVa + etc. I

Gbatings IN' Theory and Practice

533

The second series of integrals will be

g4Z)(Aa? + Mv) L 4- + etc. }

The total integral will then be
sin n

— ■*" j^l + 4. etc.J

As before, inultiply this by the same with the sign of i changed to
get the intensity.

Example 1. — ^Bqtjal Distances

The space, a, contains n' — 1 equidistant grooves, so that y^ = y 2 — Vx

= etc., = i
w

metals with some one metal, such as iron. Making the iron spectrum

sin

idii

Hence the displacement becomes

tafi

sin n
sin

As the last term is simply the integral over the space in a different

form from before, this is a return to the form we previously had except
that it is for a grating of nn' lines instead of n lines, the grating space
a

Example 2. — Two Grooves

l + flaw.=26^co8^>.

But 6a/£ = 2 JVir. Hence this becomes

26^^ ^a^cos Trivi^ .*
a

The square of the last term is a factor in the intensity. Hence the
spectrum will vanish when we have

JV^ = i,f,4,etc/

^ A theorem of Lord Ra7lelj!:h*8.

534

Hbnbt a. Eowland

la 3 a
^-T 1^’ 3 yi’

5 a

T yT’

etc.

Thiis when — = 3, the Ist, 3d, etc., spectra will disappear, making
Ux

a grating of twice the number of lines to the cm.

■WTien — =4, the 3d, 6th, 10th, etc., spectra disappear. When
Vi

iL = 6, the 3d, 9th, etc., spectra disappear.

The case in which — = 4, as Lord Eayleigh has shown, would he very

nsefol as the second spectrum disappears leaving the red of the first
and the ultra violet of the third without contamination by the second.
In this case two lines are ruled and two left out. This would be easy
to do but the advantages would hardly pay for the trouble owing to
the following reasons: Suppose the machine was ruling 20,000 lines
to the inch. Leaving out two lines and ruling two would reduce the
dispersion down to a grating with 6000 lines to the inch. Again, the
above theory assumes that the grooves do not overlap. Now I believe
that in nearly, if not all, gratings with 20,000 lines to the inch the
whole surface is cut away and the grooves overlap. This would cause
the second spectrum to appear again after all our trouble.

Let the grooves be nearly equidistant, one being slightly displaced.

In this case j/i = | +

cos

rr — ^ = cos -JT- cos — Sin sm

a \ % a 2 a )

For the even spectra this is very nearly unity, but for the odd it
becomes

Hence the grating has its principal spectra like a grating of space ^

but there are still the intermediate spectra due to the space a, and of
intensities depending on the squares of the order of spectrum, and the
squares of the relative displacement, a law which I shall show applies
to the effect of all errors of the ruling.

This particular effect was brought to my attention by trying to use
a tangent screw on the head of my dividing engine to rule a grating
with say 28,872 lines to the inch, when a single tooth gave only 14,4:36
to the inch. However carefully I ground the tangent screw I never was

Gratings in Theory and Praotiob

635

able to entirely eliminate the intermediate spectra due to 14,436 lines,
and mate a pure spectrum due to 28,872 lines to the inch, although I
could nearly succeed.

Example 3. — One Groove in m Misplaced

Let the space a contain m grooves equidistant except one which is
displaced a distance v- The displacement is now proportional to

1 + + flWbM-s- + eto.+ + + etc. +

hfxa

ifia

Multiplying this by itself with — -i in place of + S adding the
factors in the intensity, we have the whole expression for the intensity.
One of the terms entering the expression will be

sin n

sin

lafj. „ haix

a Sg/t - OT + 1

bap. oiYi ^ ^

Bin

^2m 2

Now the first two terms have finite values only around the points
mNr:^ where mJT is a whole number. But %p — m -f- 1 is also a

whole number, and hence the last term is zero at these points. Hence
the term vanishes and leaves the intensity, omitting the groove factor,

bap

sin* n -g-

- bap
sin^

. 9 bap

sm’ n ■ '

sm’

The first term gives the pjiuicipfil spcctm as clue to a giutmg space
of - and number of lines tm as if the grating were perfect. The last

term gives entirely new spectra dne to the grating space, a, and with
lines of breadth dne to a grating of n lines and intensities equal to

(p/ivy.

Hence, when the tangent screw is used on my machine for 14,436
lines to the inch, there will still be present weak spectra due to the
14,436 spacing although I diould rule say 400 lines to the mm. This
I have practically observed also.

The same law holds as before that the relative intensity in these

536

Hbnby a. Eowland

subsidiary spectra varies as the square of the order of the spectrum and
the square of the deviation of the line, or lines from their true position.

So sensitive is a dividing engine to periodic disturbances that all the
belts driving the machine must never revo*lve in periods containing an
aliquot number of lines of the grating; otherwise they are sure to make
spectra due to their period.

As a particular case of this section we have also to consider

Periodic Errors op Euding. — Theory op Ghosts ”

In aU dividing engines the errors are apt to be periodic due to

drunken ” screws, eccentric heads, imperfect bearings, or other causes.
We can then write

y zs sin (ein) + sin (ajw), -f etc.

The quantities Sj, etc., give the periods, and ^i, ag, etc., the ampli-
tudes of the errors. We can then divide the integral into two parts as
before, an integral over the groove and spaces and a summation with
respect to the numbers.

S (is =r tZa .

Jyl t/o

It is possible to perform these operations exactly, but it is less com-
plicated to make an approximation, and take y" — y' = g, a constant
as it is very nearly in all gratings. Indeed the error introduced is
vanishingly small. The integral which depends on tho shape of the
groove, will then go outside the summation sign and we have to per-
form the summation

aon + d] slneiTi + Os sin e^n + etc. [ .

Let be a BesseTs function. Then

cos {u sin ^p) = 7o (u) + 2 [7* (u) cos* + 7* (u) cos* ^ + etc.]
sin (u sin ^p) = 2 [7i (u) sin ^ + 7, (w) sin® ^ + etc.]

But sin^p — eos (u sin -- i sin (u sin .

Hence the summation becomes

s <

Cb/iaon

X [Jo (ifJ-Oi) + 2 (- i7i (ifiOi) sin e^n + 7, (tfiOi) cos 2ein - etc.)]
X [Jo (ifj-ao) H- 2 (- iJj (bfiaO sin e^n + 7, cos %e^n — etc.)]
X [Jo (Sa^s) + etc.]

X [etc.]

Gratings in Theory and Phaoticb

637

Case I. — Single Periodic Error
In this case only o# and exist. We have the formula

sin-f-

Hence the expression for the intensity becomes

I + 6tc.

As n is large, this represents various very narrow spectral lines whose
light does not overlap and thus the different terms are independent of
each other. Indeed in obtaining this expression the products of quan-
tities have been neglected for this reason because one or the other is
zero at all points. These lines are all alike in relative distribution
of light and their intensities and positions are given by the following
table:

Places.

Intensities.

Deslgnatlone.

Primary line

Ji ( Wi)

Ghosts of 1st order.

Ghosts of 8d order.

-H

Ghosts of 3d order.

etc.

Hence the light which would have gone into the primary line now
goes to making the ghosts, so that the total light in the line and its
ghosts is the same as in the original without ghosts.

The relative intensities of the ghosts as compared with the primary
line is

sin n

i/Mt

sin

8in«- ^ -g \±it

Sin n

bfidQ —
2

8in^ ?»gr/’»

538

Hbnbt a. Eowlaitd

This for very weak ghosts of the first, second, third, etc., order,
becomes

The intensity of the ghosts of the first order varies as the square of
the order of the spectrum and as the square of the relative displace-
ment as compared with the grating space This is the same law as
we before found for other errors of ruling, and it is easy to prove that
it is general. Hence

The effect of small errors of ruling is to produce diffused light around
the spectral lines. This diffused light is svibtracted from the light of the
primary line, and its comparative amount varies as the square of the
relative error of ruling <md the square of the order of the spectrum.

Thus the effect of the periodic error is to diminish the intensity of
the ordinary spectral lines (primary lines) from the intensity 1 to
and surround it with a symmetrical system of lines called
ghosts, whose intensities are given above.

When the ghosts are very near the primary line, as they nearly always
are in ordinary gratings ruled on a dividing engine with a large number
o-f teeth in the head of the screw, we shall have

Ji + 2 ^) + Jiioi “ 5 ^) = 2Ji“5a5,;t nearly.

Hence the total light is by a known theorem,

j;»+etc.] = l.

Thus, in all gratings, the intensity of the ghosts as well as the
diffused light increases rapidly with the order of the spectrum. This
is often marked in gratings showing too much crystalline structure.
For the ruling brings out the structure and causes local difference of
ruling which is equivalent to error of ruling bb far as diffused light is
concerned.

For these reasons it is best to get defining power by using broad
gratings and a low order of spectra although the increased perfection of
the smaller gratings makes up for this defect in some respects.

There is seldom advantage in making both the angle of incidence
and diffraction more than 45°, but, if the angle of incidence is 0, the
other angle may be 60°, or even 70°, as in concave gratings. Both
theory and practice agree in these statements.

Ghosts are particularly objectionable in photographic plates, especi-

GsATIiTGS IK ThEOKT AND PeAOTIOB

539

ally when they are exposed very long. In this case ghosts may be
brought ont which would be scarcely visible to the eye.

As a special case, take the following numerical results:

JV=

a-, 1

|iO

60 ’

100

25’

'So’

100

26’

60’

100’

.ap

252’

1008

V6’

63’

2?2

7 ’

28’

102 •

In a grating with 20,000 lines to the inch, using the third spectrum,

ft 1

we may suppose that the ghosts corresponding to = ra "wiH he visible

ft 1

■ and those for ^ very troublesome. The first error is ax ==-nnrfinnr

in. and the second = g g oVo ' o ^^ce a periodic displacement of
one millionth of an inch produce visible ghosts and one five hun-
dred thousandth of an inch will produce ghosts which are seen in the
second spectrum and axe troublesome in the third. With very bright
spectra these might even be seen in the first spectrum. Indeed an over
exposed photographic plate would readily bring them out.

When the error is very great, the primary line may be very faint or
disappear altogether, the ghosts to the nmnber of twenty or fifty or
more being often more prominent than the original line. ThuS;, when

dflffx = 2-405, 5-52, 8-65, etc. = 2!tlV JIl ,

Cto

the primary line disappears. When

iMOx^O, 3-83, 7-02, etc. = 2;: JV ,

the ghosts of the first order will disappear. Indeed we can make any
ghost disappear hy the proper amount of error.

Of course, in general

Thus a table of ghosts can be formed readily and we may always tell
when the calculation is complete by taking the sum of the light and
finding unity.

540

Henet a. BowiiAnd

% nN .

Jl.

/xi

Jii

1-000

•3

•980

•010

•4

-933

•088

•883

.082

•003

•8

•716

.186

•006

1-0

-586

•194

•013

3*0

-060

-888

•124

•017

•001

3-605

•000

•269

•186

•040

•008

•068

•116

•386

•095

-017

•002

8-883

•163

•000

•162

•176

•066

•018

•003

4-0

•158

-004

•188

•185

•079

•018

•002

• . ■

5-0

•081

•307

•002

•188

•168

•068

•017

•003

6-530

•000

•116

etc .

6-0

•033

•077

•069

•018

•138

•181

•061

-017

•008

...

7-016

.000

•090

etc .

•039

•055

•018

•086

-Oil

•086

-114

•108

•050

•016

•001

8-654

•000

•076

etc .

10-

-060

•003

•066

•008

•066

•003

•047

•101

•091

•051

•033

•oil

■009

•033

This table shows how the primaiy liae weakens and the ghosts
strengthen as the periodic error increases, becoming 0 at = 13-405.

It then strengthens and weakens periodically, the greatest strength
being transferred to one of the ghosts of higher and higher order as
the error increases.

Thus one may obtain an estimate of the error from the appearance
of the ghost.

Some of these wonderful effects with 20 to 60 ghosts stronger
the primary line I have actually observed in a grating ruled on one of
my machines before the bearing end of the screw had been smoothed.
The effect was very similar to these calculated results.

Dottbm Pbbiodio Eeeob

Supposing as before that there is no overlapping of the lines, we
have the following:

Placet . IntentitUt .

I Primary line.

= , i ± [ J , (5(v«,)]»

Ghosts of 1st order.

Qbatinqb in Theobt and Pbaotioe

541

Places,

Intensities,

t 61 zt 69

c7i

■H

{.Jtiboyfit) Ji (}a,/j*)]’

[/, (baifit) J, (batfi,)y

1 6\ db

= A* ± Jx (iffsM,)?

etc.

Ghosts of 3d order.

^ Ghosts of 3d order.

Each term in this table of ghosts simply expresses the fact that each
periodic error produces the same ghosts in the same place as if it were
the only error, while others are added which are the ghosts of ghosts.
The intensities, however, are modided in the presence of these others.
Writing = la^ and c, =

The total light is

Jn<^) +

+ etc.

which we can prove to he equal to 1.

Hence the sum of all the light is still unity, a general proposition
which applies to any number of errors.

The positions of the lines when there is any number of periodic
errors can always be found by calculating first the ghosts due to each
error separately; then the ghosts due to these primary ghosts for it as
if it were the primary line, and so on ad infinikm.

In case the ghosts fall on top of each other the expression for the
intensity fails. Thus when a,‘=3ai, etc., the formula virill

need modification. Tho positions are in this case only those due to a
single periodic error, but the intensities are very different.

Places.

ba.

IntmstU&i.

/4=:

542

HBNEy A. EowiiAnb

Places.

etc.

IntenftitAes.

+ [e/i {ba-itJ.^ Jx Js (5^2 A*i) + etc.]*,

etc.

We have hitherto considered cases in which the error could not be
corrected by any change of focus in the objective. It is to be noted,
however, that for any given angle and focus, every error of ruling can
be neutralized by a proper error of the surface, and that all the results
we have hitherto obtained for errors of ruling can be produced by errors
of surface, and many of them by errors in size of groove cut by the dia-
mond. Thus ghosts are produced no>t only by periodic errors of ruling
but by periodic waves in the surface, or even by a periodic variation in
the depth of ruling. In general, ho-wever, a given solution will apply
only to one angle and, consequently, the several results will not be
identical; in some cases, however, they are perfectly so.

Let us now take up some cases in which change of focus can occur.
The term kv* in the original formula must now be retained.

Let the lines of the grating be parallel to each other. We can then
neglect the terms m z and can write r® = very nearly. Hence the
general expression becomes

gift (V* + MV— *!/>)£?* J

where k depends on the focal length. This is supposed to be rery
large, and hence x is small. -

This integral can he divided into two parts, an integral over the
groove and the intervening space, and a summation for all the grooves.
The first integral will slightly vary with change in the distance of the
grooves apart; hut this effect is vanishingly small compared with the
effect on the summation, and can thus he neglected. The displace-
ment is thus proportional to

Case I. — ^Linbs at Vasiaklb Distances
In this case we can write in general

y = an + Oit? + Ujn* 4 - etc.

As K, tty fflg, etc., are small, we have for the displacement, neglecting
the products of small quantities,

i’e® [m (on + oi«» + o,n» + etc.)— *o‘n»].

Gratings in Theory and Practice

543

Hence the term can he nentralized hy a change of forms ex-
pressed hy;/ai = «a®. Thus a grating having such an error will have
a different focus according to the angle n, and the change will he + on
one side and — on the other.

This error often appears in gratings and, in fact, few are without it.

A similar error is produced by the plate being concave, but it can
he distinguished from the above error by its having the focus at the
same angle on the two sides the same instead of different.

According to this error, the spaces between the lines from one
side to the other of the grating, increase uniformly in the same manner
as the lines in the B group of the solar spectrum are distributed. For-
tunately it is the easiest error to make in ruling, and produces the least
damage.

The expression to be summed can he put in the form
2'^Man I j (jiQ^ — fjf + ibiua^ H- H [fittz + ib w* 4* etc.]

The summation of the different terms can he obtained as shown
below, but, in general, the best result is usually sought by changing
the focus. This amounts to the same as varying k until — « a® = 0
as before. For the summation we can obtain the following formula from
the one already given. Thus

'Vl-
*^0

sin
sin p

;n— 1).

Hence

sin np
sin IP '

When n is very large, writing = pn = icNn + q, wre have

c = Sf/zOi — ica®),

(/ — ,

o" = i [/la, + ib (jxUi — ,

c"' = etc.,

Whence writing

544

Henry A. Eowland

the STiPunation is

4-4c" ^

+ etc.

d sinq _ q oosq — sin q

Iq q ~ q'

<P sin q — 2g COB y + (2 — g*) sin y
^ q q* *

<P sin q _ g (6 — g*) COB g — (6 — 3g*) sin q
dq' q g* ’

etc. etc.

These equations serve to calculate the distribution of light intensity
in a grating with any error of line distribution suitable to this method
of expansion and at any focal length. For this purpose the above
Bummation must be multiplied by itself with + 1 in place of — i.

The result is for the light intensity

As might have been anticipated, the effect of the additional terms is
to broaden out the line and convert it into a rather complicated group
of lines, as can sometimes be observed with a bad grating. At any
given angle the same effect can be produced by variation o1£ the plate
from a perfect plane. Likewise the effect of errors in the ruling may
be neutralized for a given angle by errors of the ruled surface, as noted
in the earlier portions of the paper.

A NEW TABLE OE STANDARD WAVE-LENGTHS

[JohnB Hopkins University Circulars, No. 106, p. 110, 1898; rhilosophioal Magazine [5],
XXXVr, 49-76, 1898 ; Astronomy and Astro-Physies, XII, 821-847, 1898]

Pbefatory Note

During the last ten years I have made many observations of wave-
lengths, and have published a preliminary and a final table of the wave-
lengths of several hundred lines in the solar spectrum.

For the pnri)ose of a new table I have worked over all my old observa-
tions, besides many thousand new ones, principally made on photo-
graphs, and have added measurements of metallic lines so as to make
the number of standards nearly one thousand.

Nearly all the new measurements have been made on a now measur-
ing machine whose screw was specially made by my process* to cor-
respond with the plates and to measure wave-lengths direct with only
a small correction.

The new measures were made by Mr. L. E. Jewell, who has now be-
come so exj3ert as to have the probable error of one setting about Yhsu
division of Angstrom, or 1 part in 5,000,000 of the wave-length. Many
of these observations, however, being made with different measuring
instruments, and before sxieh experience had been obtained, have a
greater probable error. This is especially true of those measurements
made with eye observations on the spectrum direct. The reductions of
the reading were made by myself.

Many gratings of G in. diameter and 21^ feet radius wore used; and
the observations were extended over about ten years.

The standard wave-length was obtained as follows: Dr. Bellas value
of was first slightly corrected and becajne 589(5 -20. 0. S. Peirce’s
value of the same lino was corrected as the result of some measurements
made on his grating and became 5896*20. The values of the wave-length
then become

iSeeEuoyc. Brit., art. Screw.

546

Henbt a. Eowlaitd

Weight Observer.

1 Angstrom, corrected by Thal&i 5805*81

2 Miiller & Kenapf 5896*25

s Eiirltauia 5895-90

S Peiice

10 Bell 6896-30

Mean .5896-156

As the relati-ve values aie more importaat for spectroscopic -work
than the absolute, I take this value -without further remark. It -was
utilized as follows:

1st. By the method of coincidences -with the concave grating, the
wave-lengths of 14 more lines throughout the visible spectrum wore
determined from this -with great accuracy for primary standards.

3d. The solar standards were measured from one end of the spectrum
to the ether many times ] and a curve of error drawn to correct to these
primary standards.

3d. Flat gratings were also used.

4th. Measurements of photographic plates from 10 to 19 inches long
were made. These plates had upon them two portions of the solar
spectrum of different orders. Thus the blue,, violet and ultra violet
spectra were compared with the visible spectrum, giving many checks
on the first series of standards.

5th. Measurements were made. of photographic plates having the
solar spectrum in coincidence with metallic spectra, often ot three
orders, thus giving the relative wave-lengths of three points in the
spectrum.

Often the same line in the ultra violet had its wav(‘-lcngth (letter-
rained by two different routes back to two different lines of the visible
spectrum. The agi-uement o-f these to division of Angstrom in
nearly every case showed the accuracy of the work.

6th. Finally, the important lines had from 10 to 30 imnisui-cincnts on
them, connecting them with their neighbors and many i)(>inls in the
spectrum, both visible and invisible; and the mean values hound the
whole system together so intimately that no changes could be inaih* in
any part without changing the whole.

This unique way of working has resulted in a tahlo of wav<f-lenglhs
from 3100 to 7700 whose accuracy might be estimated as follows:

Distribute less than division of Angstriini pro])erly iliroughout

A New Table of Standard Wave-Lengths

547

the table as a correction, and it will become perfect within the limits
2400 and 7000.

The above is only a sketch of the methods used. The complete de-
tails of the work are ready for publication but I have not yet found any
journal or society willing to undertake it.*

[The tables of wave-lengths are omitted.]

* [These details were Anally published in the Memoirs of the American Academy of
Arts and Sciences, XII, 101-186, 1896, under the title, ‘ On a Table of Standard Wave-
Lengths of the Spectral Lines.’]

ON A TABLE OF STANDAED WAVE-LENGTHS OF THE
SPECTRAL LINES*

IMemoira of the American Academy of Arts and Sciences, XII, 101-186, 1896]
Pbbsbnted Mat 10, 1893

iHTeBtigatlons oa Light and Heat, made and published wholly or In part with appro-
priation from the Rnmford Fund

Some years since, having made a machine for ruling gratings and dis-
covered the concave grating, which placed in my hands an excellent
process for photographing spectra, I applied myself to photograph the
solar spectrum. The property of the concave grating, mounted in the
method which I use, of producing a normal spectrum gave mo the
means of adding a scale of wave-lengths, and so producing a photo-
graphic map of the solar spectrum on a very large scale and of great
accuracy. I soon after constructed a very much better ruling engine,
which is kept at a uniform temperature in the vault of the new physical
laboratory of the Johns Hopkins University, with which I have rnadet
very much better gratings. I therefore went over the whole process
once more, extending the map to include and making new nt^gatives
of the whole spectrum very much better than the old. This sot of ten
photographic plates is now familiar to most spectroscopists.

In order to place the scale on the negatives, it was necessary to know
the wave-lengths of certain standard lines. Of course my fimt thought
was of Angstrom, whose measurements were the wonder of his time.
On trying to place my scale according to his figures, I found it impos-
sible to make them and my photographs agree; and I finally was forced
to the conclusion that a new series of standards was needed before^ I
could go further. Here again the concave grating came to my rc^seme.
All the spectra are in focus at once, and relative measures cau thus be
made at once hy micrometric measures of the overlapping spectra.
Again, the spectrum is normal, and so a micrometer of very long range
could he used. To obtain the primary standards by means of oven-lap-
ping spectra, I have used gratings with from 3000 u]> to 20,000 lines to

1 An abstract of this paper has recently appeared In ‘Astronomy and Astro-Physics,*
and In the ‘London Philosophical Magazine.*

Table oe Staneahe WAVE-LBNaTiis op tjie SrpcTHAL Lines 5-49

the inch, and from 13 to feet focus. The first scries inado witli the
13-foot grating by Mr. Koyl in 1882 was not found quite accurate
enough, and I liavo made personally a long series 'with gratings
of 214- feet focus which is much niori^ accurate. Those Imig focus grat-
ings liad from 7000 to 20,000 lines to the inch, and wore ruled on two
dividing engines, while the 13-foot one had a less nuinher, possibly
3000. There are tw'o prineipal errors to guard against in this method,
the iirst peculiar to the metliod of coincidences, and the second to any
method whore gratings are uaed.“ The first is that, whore spectra are
over each other and the lines therefore often on top of each other, the
line of one spectrum may bo apparently sliglitly displaced by the
I)resencc of one from another spectrum, although tlu^ latter may be
almost invisible. The use of ])rojK»r absorbents obviates this difiiculiy.
The second source of error is more subtle, and arises from tlio diamond
ruling differently on dilferent parts of the grating. It is more apt to
occur in concave gratings than plane ones, although few are porfecd-ly
free from the error, as it is very difficult to get a diamond to rule a
concave grating uniformly. Looking at the grating in spectra oE
dilTorent orders, the grating may appear uniform from (md to end in
one, and ])ossil)l 3 ^ brighter at one end than the other in anollier spec-
trum. This gives a (dianco for any imperr(‘(dion in the form of tho
surface of tho grating, or any errors in its ruling, or indeed the spheri-
cal aberration of the lenses or concave grating, to affect tlu^ nuMisure-
tiiont of relatives wave-lengidi.* This c^rror I hav(^ guar(I(*d against hy
using only uniformly ruled gratings, reversing them, and using a great
number of them. I Inivo also used tlio (^oincidem^e of only the lower
orders of spectra, such as the 2d, 3(1, 4th, 5th, and (ith. (loimddences
up to tho 12th we^(^ however, observed hy Mr. Key! witli the 13-foot
eon(*av(‘, and probably havc^ some (‘vrors of this naturcL

In Ibis way I (^siahlished about nft(am poinis in th(‘ visible spcudnim
wliich served as primary standards. These! wcto so int(^rwov(ui by Ihcj
coin(*idenc('H that I hav(‘ gtvat coufi(lenc(^ in i.h(‘ valine of inosl of them.

■-* The variation of tho diaporBion of tho air with tlu^ thermometer aiul barometer
ia probably not worth consickriiijf^ for the visible part of the Bpectrum, althou^fh It
mi^^ht he worth investi#?atin|u: for tho two oxtromitiea of tho Bpcctrum.

8 Tho error of nsinju: irratin#»;s of variable briKhincflH In dliferont parts, or those
with Imporfeot nillnjj: of any kind, f have oonstantly #cuardoa against. Such I be-
Uevo to be the principal causos of tho groat errors In relative and absolute wave-
lengths in Vogel’s tables, as the gratings ho iisod, made by Wandschaft, wore full of
errors of all kinds.

650

Hbnbt a. Eowland

Indeed, no process of angular measurement could approach the accuracy
of this one.

Thus, using a line P to start with, I determine other grou])a of lincH,
a', V, d, d', etc. From these again I find groups, some of wliich may
he the same as the first; then again from these, other groups. The
process can he continued further, but we are apt to come hack to tlu*
same linos again, and we are further limited hy the visibility of tlm
lines. Thrrs the limit of great accuracy by eye observation in eith(»r
direction is practically 4300 and 7000; although in a dark room, es{)t*ci-
ally in the first spectrum, one can see much further, even beyond the A
group, although it is difficult to set on the lines, and one is apt to mis-
take groups of lines for single lines.* When one uses a group as a
standard, and one or more of the group is an atmospheric line whi<!h
varies, the measures will of course vary also, unless the atmospheric
line is in the centre of the group. This is a very common source of
error, and has caused mo much trouble. In a grating with a very
bright second si)eetruin, T have, however, obtained the C(Mncid<*nc(f of .1
with the region whose wavo-longth is about 6080, and have thus con-
firmed the value given in my preliminary table, which was obtained by
a very long interpolation passing from the first into the sccfond spw-
trum.

The accuracy of those primary standards can be (\stimat(‘d from the
equations given in Table VTI. Tt is there seen that' there is scarc'cly
any difference in the different nioasures as derived from di(T((r«mt liiu's.

It is to he specially noted that the wave-length of P atid the lines
directly determined from it have no more weight than any of the
others. The table might just as well have been arrangcal with the /t
line, or any other, first. The true way of discussing the results is to
form a series of linear equations, about twenty-six in all, and solve*
them. This is the method I have used, although T have not dis<‘ussed
them by the method of least squares.’

Some miscellaneous observations not included in tin* tabh* allow'cd
me to add a few more linos to these primary standards.

Having completed those primary standards, I tlmn observed sev(‘rnl

*Id a very brlf^ht gratinf; I bare faintly saen, and even meaenrod, lines down to
wave-length 8600. My aBBistant, Mr. L. B. Jewell, can see far into what la called
the ultra ylolet, even to wave-length 8600 or heyond.

“The calcnlationfl of this paper have involved abont a million llgures, of which T
have personally written more than half. Hence I am not anxious for more labor of
this kind.

Table op Standard Wave-Lengths op the Spectral Lines 551

hundred standard linos in the visible spcctruni, including these primary
standards, with a inicromotor having a range of five inches, and very
accurately made. The spectrum being strictly normal, the readings so
made were proportional to the wave-length. They conld have been used
s im ply to interpolate between the primary standards, but I preferred
another method. The readings of the micrometer were made to over-
lap, so that, by adding a constant to each set, a continuous series could
be formed for the whole spectrum wdiich would bo proportional to the
wave-length except for some slight errors due to the working of the
ap]) 4 iratus for keeping the focus constant. Making this series coincide
with two standards at the ends, the wave-lengths of all could be obtained
by simply multiplying the whole series by one number and adding a
constant. This usually gave the wave-lengths of the whole &i>eetrum
witliin OT or 0*^ divisions of Angstrom. The difEcrencos of this series
from the primary standards were then plotted, and a smooth curve
drawn through the points thus found. The ordinates of this curve
then gave the correction to be applied at any point.

It is to be noted that the departure from the normal spectrum was
very small, and the correction thus found wasWery certain. The cause
of the departure was not apparent^ but may have lK^en the sliglil tilting
of the spectrum, by which it was measured somewhat obliquely at
places.

The visible spectrum was thus gone over five or more times in this
manner, with several different gratings and in diiferent orders of sjiectra.
The results are given in Table X, Columns (7, B, p, q, m, 0, 7i, % etc.
The spectrum from the green down to and including A was also ob-
served on a largo instrument for flat gratings, having lenses six and
one-half inches in diameter and of eight feet focus. Those latter
observations are marked G\ This region I intend at some future time
to observe further.

It was now required to 0 'l>servG the ultra violet to eomploto the series.
For this purpose the coincidences oE the 2d, 3(1, 4th, Hth, and Gth
s]>eetra of a 7000, 21^ feet radius, grating wore ])hotographed. My in-
strument will take in photographic plates twenty inches long, hut there
will he a slight departure from a normal spectrum in so long a plate.
Hence plates ten inches long wore mostly used for this special series.
Before the camera was y)lacofl a revolving plate of metal about three-
sixteonths of an inch thick, and having a slit in it of the smne width,*

This is described in the Johus Hopkias Circular of May, 1880, by Dr. Ames.

662

Henry A. Howland

When the flat side was parallel to the camera plate, a strip of tho
spectrum three-sixteenths of an inch wide fell on the plate. When
turned ninety degrees, the plate shielded this portion and exposed tho
rest. Using absorbents, it was thus possible to photograpli a strip of
say the 4th spectrum between two strips of the 5th. This arrangement
is better than having only two edges come together. To correct any
movement of the apparatus during the time of exposure, I expose on
one spectrum, then on the other, and back again on the first.

Placing the negatives so obtained on a dividing engine with a micro-
scope of very low power and a tightly stretched cross-hair, the coin-
cidence of the two spectra can be measured. Owing to the large scale
of the photographs,— about that of Angstrom,— ah ordinary dividing
engine having errors not greater than-ruVo" i^ch can bo used, but tho
negatives should be gone over at least twice, reversing them orid for
end. Two screws were used in the engine and finally another com-
plete machine was constructed, giving wave-lengths direct with only a
slight correction. For dcteimining the wave-length of metallic lines,
the same .process can be used with wonderful accuracy.

The results are given in the columns marked P2. with tho number
of the plates. The accuracy is very remarkable, and I think tho liguros
establish the assertion that the coincidence of solar and metallic lines
can be determined with a probable error of one part in t50(),0()0 by only
one observation.

This process not only gave me measures of the ultra violet, but also
new observations of the visible spectrum. So far in my work on these
coincidences, I have only used crythrosin plates going a little Ixdovv T> ;
but cyanine plates might be used to B, or even in tho ultra nul, as Trow-
bridge has recently shown. One plate, No. 20, however, eonnocts wave-
lengths 6400 and 3200.

Thus I have constructed a table of about one thousand linos, more
or less, which are intertwined with each other in an iinm(‘nse minil)er
of ways. They have been tested in every way I can think of during
eight or nine years, and have stood all the tests; and I think T (^an
present the results to the world with confidence that the n^sults of tho
relative measures will never be altered very much. 1 believer tlial no
systematic error in the relative wave-lengths of more than about ±‘01
exists anywhere except in the red end as we approach A. Possibly
± -03, or even less, might cover that region.

The relative measures having thus been obtained, wo have means in
the concave grating of obtaining the wave-lengths of the lines of metals

Table op Standard Wave-Lengths op the Spectral Lines 553

to a degree of accuracy liitherto unknown, and thus of solving the great
problem of the mathematical distribution of these lines.

But for the comparison of spectra, as measured by different observers,
some absolute scale is needed. Hitherto Angstrom has boon used.
But it is now very well known that his standard measure was wrong.
As his relative measures are also very wrong, I have concluded that the
time has come to change not only the relative measures, but the abso-
lute also. To this end Dr. Louis Bell worked in my laboratory for
several years with the best apparatus of modern science, using two
glass and two speculum metal gratings, ruled on two dividing engines
with four varieties of spacing, three of which were incommonsurahle
or nearly so, with two spoetroiuoters of entirely different form, with a
, variety of standard bars compared in this country and in Europe, and
with a special comparator made for the measure of gratings. His result
agrees very well with the next beat determination, that of Mr. 0. S.
Peirco of t^ U. S. Coast Survey. His final result agrees within 1 in
50,000 with his preliminary value.^ This most recent value, combined
with those of Peirce, Muller and Kemjvf, Kurlbaum and Angstrom, I
have adopted to rodiice iny final results to, although the calculations are
made according to Boll’s preliminary value. See Appendix A.

But it rests with scientific men at large to adopt some absolute
standard. TFlie absolute standard is, of course, not so important as the
relative, and possibly the average of Angstrom might be adopted. But
for myself I do not believe in continuing an error of this sort indefi-
nitely. All the results obtained before the concave grating (taiuo into
use were so imperfect, that they must he replaced by others very soon.
With a good concave grating one man in a few years could obtain the
wave-lengths of tlie cloinonts with far greater accuracy than now
known.

As an aid to this work, T have constructed the tal)Io of wavc-longths
given in this pajior, which have already been adopted by the British
Association and by the most noted writers of Oerinany and other
(^ount^ios, and sincerely hope that it will aid in Iho work of making
the wave-length of a spectrum line a definite (piimtity within a few
hundredths of a division of Angstrom.

Absolute Wave-Length ok J)

The following is an estimate of the absolute wave-length of the J) line
from the best determinations. First, I shall recalculate the portion of

American Journal of Science, 1887.

664

Henby a. Eowland

Dr. Bellas paper “ in which the calibration of the grating space is taken
into account. The method of correction is founded on the principle
that a linear error in the spaces only affects the focal length, and not
the angle, and that small portions which have an error, and thus throw
the light far to one side, should be rejected. The corrections Dr. Bell
has used seem to me very proper, except to grating III, which appears
to me to be twice too great. I find the following :

Orating.

Correction.

Pinal Values.

6896-20

— -02

5896-18

II.

5896-14

+ -09

6896-23

III.

5896-28

— -06

6896-22

IV.

5896-14

+- -03

5896-1'}'

Moan value, 6896-20.

This is very nearly the value given by Dr. Bell.

The determination of Mr. C. S. Peirce of the U. S. Coast Survey is
certainly a very accurate one. Dr. Bell and myself have made some
attempts to calibrate his gratings, which he sent to us for the purpose,
and to correct for the scale used by him. There is great uncertainty
in this process, as we had only a portion of the necessary data. The
correction of his scale was also uncertain, because the glass scales used
by him may have changed since he used them, in the manner thermom-
eter bulbs are known to change. Correcting, then, only for the error of
ruling in the gratings, we have :

Peirce^B value 5896-27

Correction* — -07

5896-20

The correction for the scale would be about as much more in the same
direction, provided the glass scales had not changed. But it is too
uncertain to be used, although I have applied it in my preliminary
paper.

Kurlbaum^s result, made with two good modem gratings, has the
defect that the gratings were 42 and 43 mm. broad, quantities which
it is impossible to compare accurately with a metre. His small objec-
tives, one inch in diameter, could not take in light from the whoh?
grating, and so the grating space was not determined from the portion

« American Journal of Science, 1888.

^Bell, American Journal of Science, May, 1888, p. 865.

Table op Standard Wave-Lengths op the Spectral Lines 555

of the grating used. The spectrometer was poor, and the errors of
the grating undeternuned.

Mliller and Kempf used four gratings, evidently of very poor quality,
as they give results which differ 1 in 10,000.

The result of Angstrom, was a marvel at the time, but the Nohert
gratings used by him would now be considered very poor. Taking
Thal6n’s correction for error of scale, we have lor the moan of tlio h
lines 5269*80, which gives, by my table of relative wave-lengths, 1) —
6895*81. It is rather disagreeable to estimate the relative accuracy
of observations made by dijfferent observers and in different countries,
but in the interest of scientific progress I have attempted it, as follows:

wt.

Angstrom 5895*81 1

Mliller and Kempf . . . .5896*25 2

Kurlbaum 5895*90 2

Peirce 5896*20 5

Boll 5896*20 10

Mean, 5896*156 in air at 20° and 760 mm. pressure.

This must be very nearly right, and I Ixilicve the wave-length to be
as well determined as the length of most standard bars. Indeed, fur-*
ther discussion of the question would involve a very elaborate discus-
sion of standard metres, a qxiestion involving endless dispute. I think we
may say that the above result is within 1 in 100,000 of the correct value,
which is very nearly the limit of accuracy of linear measurements. This
should be so, as the probable error of the angular measures alteets tho
wavc^-longth only to 1 in 2,000,000,'" and hence nearly the whole accuracy
rests on the linear measures.

Besume op Process for Obtaining Relative Wave-Lengths

1. Determination of about 20 lines in the visible spectrum by coin-
cidences by Koyl.“

w Is not a grating and spectrometer thus tho best standard of length, and almost
independent of the temperature? Gratings of 10 cm. length can now be ruled on
my new engine with almost perfect accuracy, as seen in the calibration of Grating
IV in Dr. Bell’s paper, and it seems to mo the time has come for their practical use.

These observations of Mr. Koyl were finally given no weight, on account of the
inferior apparatus used. They serve a useful purpose, however, as checks on the
other work.

556

Henet a. Rowland

2. DeterminatioE of about 15 lines in the visible spectrum by coin-
cidences by Rowland, using several gratings of 21^ feet focus.

3. Interpolation by direct eye observations with concave gratings of
Sl'J feet focus and micrometer of 5 inches range and of almost perfect
accuracy.

4. Interpolation by means of flat gratings.

5. Measurement of photographic plates from 10 to 19 inches long,
having two or three portions of the spectrum in different orders on
them, thus connecting the ultra violet and blue with the visible spec-
trum. The fact that nearly the same values are obtained for the violet
and ultra violet by use of different parts of the visible spcctnun proves
the accuracy of the latter.

6. Measurement of photographic plates having the solar visible spec-
trum in coincidence with the metal lines of different orders of spectra.
The fact that the wave-lengths of the metal lines are very nearly the
same as obtained from any portion of the visible or ultra violet spec-
trum proves the accuracy of the latter, as well as that of the metallie
wavelengths.

7. Measurement of plates having metallic spectra of different orders.

Advantages oe the Pkooebs

The only other process of obtaining relative wave-lengths is by
means of angular measures. Supposing the angle to be about 45°, an
error of 1" will make an error of about 1 in 200,000 in the sine of the
angle. When one considers the changes of temperature and barometer
measuring on one line and then another, together with the errors of
graduation, it would be a difficult matter to measure this anghs to 2",
making an error of 1 in 100,000, or about division of Angstr'om.

Looking over the observations of principal standards maile under
the direction of Professor Vogel in Potsdam, with very poor gratings
but an excellent spectrometer, we find the average probable error to
be, about db YBvVinr 0^ the wave-length, which is not far from the other
estimate. This does not include constant errors, and I believe the
probable error to be really greater than this.

The method of coincidences by the concave grating gives far superior
results. The distance to be measured is very small, and the e(pii valent
focal length of a telescope to correspond would be very great (21^
feet). Furthermore, all changes of barometer and thermometer are
eliminated at once, except the small effect on the dispersion of the air,
which, when known, can be corrected for. It is not to bo wondered at

Table oe Standard Wayb-Lengths op the Speoteal Lines 56 ?

that this method is far superior to the former. The probable error is,
indeed, reduced to iiTwhnnr? less for the best* linos. Where

the interpolation can be made on photographs, this prol>ablc error is
scarcely increased at all; but oven taking it at twice the above estimate,
the method even then remains from three to five times as accurate as
that of angular measurement. Indeed, the impression made on my
mind in looking over VogeFs Potsdam observations is, that my tables
and process are ten times as accurate as theirs; and I think any careful
student of both processes will come to a similar conclusion.

The wonderful result that can be obtained by the meaBurement of
photogra))hs on the new micrometer, which can measure plates over
twenty inches long, is partly seen in the table. Where the distance is
only a few inches, the wave-length of a series of lines can be measured
with a probable error of loss than -j-J-g* of a division of Angstrom.
Indeed, a series would dotonnine any lino so tliat the probable error
would bo even i-OOOOOOl of the whole. This would detect a motion
in the line of sight of db 140 feet per second I

From tlio t(‘KtB I have made on my standards, I am led to bdlicvo
that down +o wave-length 7000, a correction* not oxcc'oding ±*01
division of Angstrom (1 part in 500,000), properly distributed, would
reduce every part to perfect relative accuracy.

To ascend to the next degree of accuracy would need many small cor-
rections whicli would scarcely pay. It is roasonaldo to assume that a
higher degree of accuracy will not be needed for twenty-five years, as
the present degree is sufficiont to distinguish tlic lines of tlu^ dilToront
clcTnonts from one another in all cases that 1 have yet tried.

Lktails op Work

To reduce all the observations in a given rc^gioii to one Hue, relative
observations extending a short distance either side of the standard
region are necessary. Thus the mean of 4215 and -^^22 (,*an Ix^ taken as
the standard, and, if only one is ol)serv(Kl, it (*an be redii(U‘d to the
standard by a correction + 3-358 or — 3-358. But it is not neeossary
to take the moan of the linos as a standard, as any one of them may
he so taken, or oven any other point wlun-e tluwo is no line, as the point
is only to be used in tlio math oniatl cal work, and finally disappears
altogether.

Table IT gives results of this nature. Tlui lcd.tors at the top of each
scries, //, h, /, etc., are the arbitrary names of the standards. The
first columns refer to the series of observations, '' Co.” being observa-

558

BLbnkt a. Eowland

tions made at the time of measuring the coincidences; Plates 9, 10, etc.,
refer to phonographic plates; 0, B, etc., refer to the series as given in
the final table, although they may differ very slightly from the latter,
as the final table contains slight corrections. Figures in parentheses
are the number of readings. The photographs were usually measured
from two to six times.

Table III gives the first series of observations made in 1884 with
a 21^ foot concave, 14,436 lines to the inch. The numbers taken for
the standards are only preliminary, and agree as nearly as practicable
with my Table of Preliminary Standards. As only differences are
finally used, they are sufidciently near. The fractions give the order
of the spectra observed.

Thus, the first observation on h and t is worked up as follows :

4691-590 7027-778

Correction to standard — 626 +^■'^'85

4690-964 7030-563

4691-590 4690-326 7027-778

—626 +-626 +2-785

4690-964 4690-952 7030-563

4691-590 7040-092

— 626 —9-547

4690-964 7030-545

Weight. h i

1 4690*964 7030*563

2 4690*958 7030*563

2 4690*964 7030*545

4690*962 7030*556

The equation 3h — 2 1 = 11*774 then readily follows.

Tables IV and V are from a 21^ foot concave with 7218 line's to the
inch, used on both sides, and thus equivalent to two p^atinp^s used on
one side only. I have not yet determined theoretically whether the
minor errors are perfectly neutralized in this manner, but it would ('vi-
dently have a tendency in this direction.

The photographic coincidences are given in the main table (X), as
not only the standards are compared by this process, hut whole regions

Table of Standard Wave-Lengths of the Spectral Lines 559

are photographed side by side. Both a 10,000 and a 20,000 concave
were used for this work.

Table VI gives the collection of the eqnatio-ns relating to the visible
spectrum, the final results being given in Table YIL

The proper method of treating these twenty-six equations would be
by the method of least s(iuares. But it would be so long and tedious,
and so liable to mistake, that I have adopted the method of starting at
one point and going forward until all the equations are reached. Thus
(liable VII), starting with an assumed value of 6, we can calculate p, n,
^ ? 0, t.

Using the eight values thus found once more, from p we have g, Tc, Z;
from n we have h, Z, g; with similar results for the others. Collecting,
we then have e, fy g, \ ft, Z, n, o, p, 5, t. Using these once more, we
have values of all the standards. We could do this any number of
times, kee})ing the proper weights, but I thought this number was suffi-
cient. The second calculation is done in the same manner, starting from
0, however, and is given in Table VITI.

The results of the two calculations are given in Table IX. Taking
the moan and adding the results of local micrometer measurements, we
obtain tlie column marked Eolative Wave-Lengths.”

Eeducdng these values by 1 part in 200,000, we make them agree
with the absolute value of the standard as before agi*eed upon. Thus
the column of standards is obtained for use in the visible spectrum.

For ordinary interpolation with the short and iin})erfect micrometers
generally used, and working with a flat grating and a spectrum not nor-
mal, the standards would be too far apart. But with such a long and
ix^rfect niicromoter as I use, and working with the normal spectruTn of
a concave gmtiug, tlicy arc entirely sufficient. However, I have filled
in tlie interval from 7();i() to 7521 by some extm siibsi^iiulards at 72r‘J().

The micrometer for eye observations has a range of five inches, and
tlie machine for measuring photographs of more than twenty inches,
both with practically i)erfoct screws made by my process. The eye ob-
servations are not an interpolation, in the ordinary sense, Imtwcen the
standards, but the whole series is continuous, the micrometer observa-
tions overlapping so that they join together to any length (l(»sired. By
measuring from the 1 ) line in one sjKJctrum to the T) lino in the next,
and including the overlap]>ing spectra, no further standards would be
necessary, asnll the lines of the speetnim would be determined at once,
knowing the wave-length of the 7 ) lino. But I usually plotted the
difference of the standards from the micrometer determination, usually

660

Hbney a. Rowland

amoimtiDg to less than one- or two-tenths of a division of Angstrom, and
so corrected the whole series to the standards. Sometimes two, or even
three, overlapping spectra were measured at once.

To make Table X, the following process was used;

1st. From all the observations at mj disposal, I determined a few
more lines around the main standards, and put them in the second col-
umn, marked 81, so that I should have a greater number of points to
draw my curve through.

3d. I then put down a few observations which were made by meas-
uring overlapping spectra.

3d. Then the main eye observations were put down as follows: —

extending from 4071 to 7040,

409(1 to 7085,

4869 to 7040,

4869 to 0079,

6866 to 0009,

6163 to 7801,

6743 to 7028,

6065 to 7671,

6866 to 7714,

6189 to 6396,

6409 to 6939,

0378 to 6833,

It.

4048 to 4834,

3d apoctrum, 14,430 grating.

tt (< (C (( ((

Ci U (( t( tt

(fragmentaryV

3d spectrum, 14,486 grating.

tt (( (( U U '

1st spoctrum, 14,436 grating.

tt (( tt tt‘ (i

plane grating.

3d spectrum, 14,486 grating.

tt tt tt tt tt

tt it (( It tt

tl t( u u u

4th- The series of photopfraplis containing coincident spectra, mostly
on plates so short as to make the spoctni nearly normal, were now in-
troduced. The plates were nuinhored from 1 to 20, Nos. T^and 19 being
rejected because imperfect

This series of plates was obtained l>y idiotographing a narrow strip
of one spectrum between two strips o-f another, the overla.p])in^^ si>octra
being separated by absorption. In order to eliminate any eliange in
the apparatus during the exposure, the latter was divided into three
parts, the first and third being given to the same s])octrum.

This series of plates gives me a continnons series of photograjdis from
wave-length 7200 to the extremity of the ultra viohit s])ec*tnnn, oacdi
part being interwoven with one or two other i)arts of the spoetruin.
Thus, ivave-leiigtli e3y00 eomos from 5200 and 5850 with only a slight
difference in values. There is scarcely any difference in any wave-
length as derived from any i>ortion of the si)cctrum; thus proving the
accuracy of the whole table. The description of the ])hites is as follows:

Table op Standabd Wave-Lengths of the Spectral Lines ' 561

Photographic Coincidences

concave, grating 10,000 LINES TO THE INCH

Spootra

Plato

Standard

4407 to 4648 and 8881

to 8486

/. g

4087

4890

8478

8667

((

4828

50C8

8612

3806

j,k

4919

5188

8688

8876

((

5050

6288

8780

4005

k , 1

((

6007

((

5888

8821

4167

k , 1

5242

((

5477

8987

4121

Ij m

((

5405

5662

4078

4222

m, n, e

5682

6816

4298

4876

«./

((

5782

((

5084

4848

4447

0 >f

((

4157

4267

8129

8218

((

4167

4825

8094

8246

8218

8818

4801

4648

8292

8478

f^g

5788

((

6977

3864

8977

6788

((

5977

8864

8984

5716

((

5977

8876

8977

((

6858

6569

8024

8267

Plates 7, 14 and 19 wore iniporfoct, owing to clouds passing over the
sun, although a part (3218 to 3318) of Plate 14 was used for interpola-
tion, as observations wore scanty in that region.

It is seen that some of the plates have only one standard upon them.
With a plang grating it would bo impossible to work them U]), but with
the normal spectrum produced by the concave grating only one is
necessary, as the niultijdier to reduce readings to wave-lengths is nearly
a constant In working uj) a whole series of plates, there is no trouble
in giving a proper value to the constant for any plate in the series
which has only one atanclai’d.

Plato 17 was measured twice by two dividing engines, and as it was
a sj)eeially good plate, eacli measure was given a weight equal to one
of the other plates. The principal error to be feared in these plates is
a displacement of the instrument between the time of the exposure on
the two spectra. This was guarded against by the inetliod above de-
scribed. In Plates 17 and 20 there was a portion of the plate on which
both the spectra fell all the time, and thus gave a tost of the displace-
ment. Tliis was found to be zero. The other plates overlap so much
that there are generally two or more determinations of each line. A

602

Henby a. Row'lakd

comparison of these values shows little or no systematic variation in the
different plates exceeding. division of Angstrom. Plates 16, 17, 18,
and 5, 6^ 8, all give the region 3900 as derived from 5200 and 5850, and
thus give a test of the relative accuracy of these latter regions. It is
seen that the two results of the region 3900 differ by about *015 division
of Angstrom. Were the wave-lengths of the region 5170 to 5270 to he
increased by *020 the discrepancy would cease. The amount of this
quantity seems rather large to be accounted for hy any displacement of
the spectra on the plates, but still this may he the cause. Again, it is
possible that different gratings may give this difference of wave-length
from the cause I have mentioned above. This cause, as I have shown,*
exists in the same degree in plane gratings as in concave. I have not
attempted to correct it in this case, hut have simply taken the moan of
the two values for the region 3900, and so distributed the en*or. This
is the greatest discrepancy I have found in the results except in the
extreme red.

Thus the region 3100 to 320(), a portion for which Plato 20 is to ho
relied upon, gives the wave-length of the ultra violet *01 division of
Angstrom higher from the region 4200 than from 6300. As the dis-
crepancies in this region before the invention of the concave grating were
often a whole division of Angstrom, I have regarded this result as satis-
factory. Indeed, until we are able to make all sorts of corrections due
to the change in the index of refraction of the air with the ’fiarometer
and thermometer, it seeins to me useless to attempt further accniucy.

With the advent of photographic plates into the table, especially the
longer ones reqTiired for metallic spectra, it becomes nec^^sary to cor-
rect them for the departure from the normal spectrum due to the use
of long plates. The plates in the box are bent to the arc of a circle of
radius r. When afterwards straightened we measure tlie distance by a
linear dividing engine. Hence, what we measure is the arc with radius r.
Let a and /9 be the angles of incidence and diffraction fro-m the grating.
We have then to express ^ in terms of d. Let X be the wave-length,
and n and W the number o-f lines on the grating to 1 mm. and the order
of the spectrum respectively. Then

^ ® sin /S ) ;

sin = A cos y9 - .

In these formulae a is the angle to the centre of the photographic
plate, and /9 and d are also measured from the centre, y is the angle

Table of Standard Wave-Lengths of the Speoteal Lutes 563

"between the radius from the centre of the photographic pleite and the
line drawn from that point to tlie centre of the grating. When prop-
erly adjusted, will be zero. Also, wc make 2 r = iJ, to obtain perfect
focus throughout. So that

Calling ^thc wave-length at the centre of the ])late, we have ap-
proximately

The first quantity, ^ value of A — A®, assuming the spectrum to

be normal. The last term is the required correction expressed in terms
of the provisional wave-length. The correction in actual practice has
been made from a plot of the correction on. a large scale, and never
amounted to more than a few hundredths of a division of Angstrom, even
for the longest plate.

In two or three plates the camera was displaced, so that ;^had a value.
In such cases no attempt was made to measure 7 , hut the plates were
only used for local interpolation by drawing a curve through certain
points used as sulwtandards.

Tlieso Hiibstaudarcls were principally used for working up the last
set of photographic plates containing the solar spectrum and the metal
spectra of the same or higher orders, or both. Some of theiri contained
three metallic spectra.

Thus the region 3900 in the solar spectrum has been obtained from
both wavc-longths 5200 and 5850. The mean of these gave values of
the wiibstandards for working \\\> the }>]ates taken at tliis point, and
containing also metallic lines at 2700.

Again, the boron linos 24.90 and 2497 have been obtained from the
regions 4800, 3200 and 3600. The mean values give substandards for
working up the metallic. s]>octrn of that region. Also the near coinci-
dence in tlic values of the wavc-longths of these lines indicate the rela-
tive accura.cy of the regions 2496, 3200, 3600, and 4800,

The use of these suhstandcwls is as follows: The ])hotographic plates,
mostly 19 inches long, were ineaHurod mostly on a mtuihinc giving wave-
lengths din^ct. l'’hc dilfcn^nccs of the results fnvm the siil standards
wore then plotted on a paper having the curve of eorrcctiou for length
upon it in such a way that the final marks should theoretically be a
straight line. This was actually the ease in all but a few plates, in

sin a + Bin

664

Henby a. Eowland

which the camera was displaced. A straight line was tlien passed through
all the marks as nearly as may be, and the correction taken ofE. This
correction could thus be obtained to division of Angstrom, and
amounted to only a few hundredths of a division at most. Possibly
division of Angstrom was the greatest correction required for length.

In this way each plate represents the average of all tlio wave-length
determinations throughout its extent, and will not admit of any correc-
tion save a linear one, should such ever be required in working over tlu*
table again.

In every plate having a solar and metallic spectrum upon it, there is
often — ^indeed always — a slight displacement. This is due either to
some slight displacement of the apparatus in changing from one spectrum
to the other, or to the fact that the solar and the electric light pass
through the slit and fall on the grating differently. In all cases an at-
tempt was made to eliminate it by exposing on the solar spectrum, both
before and after the arc, but there still remained a displacement of
T^ir ’to rhr division of Angstrom, which was determined and corrected
for by measuring the difference between the metallic and coinciding solar
lines, selecting a great number of them, if possible.

The changes from sun to arc light are much more extensive than from
one order of solar spectrum to another. In two cases I have tested thi^
latter and found no displacement, and have no fear that it exists in
the others.

In working up the plates, I have started at the plates wliose coiitro is
at wave-length 4600, and proceeded either way from that point. For
this purpose I have used the plates originally obtained for metallic
spectra^ generally using the lines due to the impurities. The method,
I believe, is obvious from the table. For a long region no suhstandards
are necessary, but are used whenever they become so.

[The tables are omitted. 1

THE SEPARATION OP THE RARE EARTHS

[Tchns Mopki7i^ Utiivenity Oirmlars^ No. 112, pp. 78, 74, 181)4]

In the course of seyeral years' investigations of the so-called "'rare
earths/' such as yttrium, erbium, holmium, cerium, etc., I have devised
several methods for their separation. I "wish to give an account of these
now, and hope soon to he able to publish a complete description of my
work and its results.

It was evident very early in the work that cerium, lanthaninm, praseo-
dymium, neodymium and thorium differed from the yttrium group, and
I have seen no reason to suppose that they can be divided any further.
All of those "earths" appear, in varying proportions, in such minerals as
gadolinito, samarslcitc, yttrialitc, cerite, etc. Besides the elements of
the cerium group hero present there are at least seven other suhstances.
For the present I shall speak of them as

a, J, % (I, Ilf Oy h.

Their properties are as follows:

PnoPKHTiMS OF Elements
Substance a

This is the principal element of yttrium and may possibly bo divided
into two in tlu^ futiiro, 8s T liavo observed a variation in tlui arc:* spec-
trum on adding potash or soda. However, this is no more evidence than
occurs in the case of iron or zirconium. I give a process below for pro-
ducing this pure.

PraperWtw.-— Ho absorption bands. Oxalate and oxide ])uro white.
It occurs in the sun. Its ])ropcTties are those of yttrium as Iiitherto ob-
tained, but I am tlio first to obtain it witl» any a]>j)roaeh to iiiirity.

Mixiwe of J, i and d

Those seem to be the princii.)al ingredients in so-called "erbium."

Oxalate is red. Oxide is pure white. Absorption band is that of
"erbium." It colors the electric arc green, and shows the "erbium"
emission bands on heating white hot. The substance 6 is strong in gado-

566

Hbnet a. Howland

linite and weak in samarskite. The solution has the absorption bands
of erbimn and most of these seem to belong to 1) rather than i, 1 1 o w-
ever, we can readily prove that the absorption bands of erbimn belong
to two substances, as we can produce a decided variation in it.

I cannot reconcile this with my spectrum work without assuming a
fourth ingredient in “ erbium."

Substance 6 is in the sun, but not i. With 1) and i the substance d
always occurs.

Substance d

This is the principal impurity of a sample of yttrium, kindly furnished
me by Dr. Kriiss, which my process of making yttrium separates out. It
has not been obtained pure, but occurs strongly in the yellow part oT
the oxides. It is in the sun.

By aid of ferrocyanide of potassium the substance a can be ol)tainc*d
pure from d. With this exception d occurs in all the preparations of
the yttrium group and cannot be separated from &, t, c, n, A, or any
of the other substances. Indeed,’! have found it in some specimens of
cerium and lanthanium, although in traces only.

On account of the trouble caused by it and its universal presence, f
propose the name demonium for it.

Its principal spectrum lino is at w. 1. 4000-6 nearly.

Substance h

This occurs mainly in samarskite. Hints toward its separation will
be given belo-w, but I have otherwise obtained none of its profxirties.

Substances n, fc and c

These always occur with d and fonn a group intermediate between the
yttrium and cerium groups. They can Ikj seimrated from tlu^se by sul-
phate of potassium or sodium by always taking in iiitcnnediate portions
of the precipitate. They seem to have a weak alworptioii spi»etnun in
the visible spectrum and strong in the ultra violet, especially L

Chemical Separation

Tlie first process that suggests itself is tliat by the sulphates of soda
or potash. This is the usual method for separating the cerium from
the yttrium groups. When the solution of earth and the sulphate
solution are both hot and concentrated, everything oxee])t some scan-
dium comes down. When done in the cold with weaker solutions, IhtUHi
is more or less complete separation of the cerium grouj). Let tlie

The Sbpakation' of the Eare Earths

567

earths he dissolved in a very slight excess of nitric acid and diluted some-
what (possibly 1 k. to 2 or 3 litres). Place in a warm place, add lumps
of sulphate of soda, and stir until no more will dissolve. Continue to
add and stir for a day or two until the absorption lines of neodymium
disappear from the solution. Filter off and call the solution No. 1.
Add caustic potash to the precipitated sulphates and wash so as to leave
the oxides once more. Dissolve in nitric acid and precipitate again with
sulphate of soda, calling the jBlltrate No. 2. Proceed in this way pos-
sibly 10 or more times. The filtrates contain less and less earths; and
the precipitate is more and more the pure cerium group; but a dozen
precipitations still leave some impurity.

The portions 1, 2, 3, etc., show decreasing “erbium^^ absorption bands,
and the spectrum shows that the substances a, &, d, i are gradually sepa-
rated out with parts 1, 2, etc., while the numerous fine lines belonging to
d, n, c, etc., with the cerium group, fill the spectrum of the portions
8, 9, 10, etc. This intermediate group has only very weak absorption
bands and evidently has three or four elements in it, as I have produced
at least that number of variations in its spectrum. The group can be
obtained fairly free from a, J, and but the substance d persists in all
the filtrates and in the precipitated cerium group also. This interme-
diate group d, n, etc., seems to be in greater proportion in samarskitc
than in gadolinite, and there seem to be more elements in samarskitc
than in gadolinite. One of these I have called h.

The oxides, especially for samarskite, are very yellow and dark.

Sulphate of ]>otasli lias a decided action in separating a and i from 6,
a and i coming down first. After two months, the solution gradually
drying, the proportion of J to a in the filtrate increased many times.
Sulphate of soda has an action of the same kind, but much woakei*.
After leaving two months over sulphate of potash and soda, tlie follow-
ing was the result of analysis of the soluble i)art as compared with the
original mixture:

(Ts,, La., etc.

Sulphate of Potash.
0

Weak

Much stronger
0

Unchanged

Weaker

Stronger

Sulphate of Soda.
0

Medium weak
Stronger
0

Unchanged
Modluta strong
Weaker

The oxide of the members of this group which arc only slightly pre-
cipitatod by tlio sulphates of soda and potash is pure snow-white, and
lienee those of h and i must he so.

568

Henry A. Eowland

The siihetance d comes down slightly sooner than a hy sulphate of
soda, hnt slightly slower by sulphate of potash. Henc(‘, in purifying
yttrium (substance a) for the last time from the ce, group, Kuli»hate of
potash will increase d in the filtrate and sulphate of soda will (l(K*roase it.

Action of oxalic acid

When the oxalates of the mixed eai*ths, free from the cc. group, are
boiled in water to which nitric acid is added, they are more or less dis-
solved, leaving a coarse, heavy, red oxalate yielding a pale yellow oxide.
The filtrate, set aside to cool, deposits more of the oxalates and l(‘av«‘s a
filtrate which contains several of the unknown elements, as also what r(^-
mains of the ce. group. On separating the ce. group the retnaiTKl(*r is
quite different from the heavy red oxalate, but there is far from comploto
separation. The analysis showed the following:

a, 6, c, d, hf iy n.

I have not found the separation particularly useful, and it seems to
more apparent than real as tested by the spectroscope.

Ferrocyanide of pota.mum

This is the most useful process and easily separates the element a,
pure and free from all others. To obtain pure a from the mineral gado-
linite, Fergusonite or SamarsToite:

First obtain the crude mixed earths in the usual manner. Then wqai-
rate the cerium group as usual until the absorption bands of neodymium
no longer appear. For the complete se]'miution without loss this must
be done several times, as much of the yttrium group is cfarried <li.)wn
with the first precipitate, as wc have before soon.

The separation of the yttrium (a) from the other elements is (dfecdcul
by precipitating the latter from a weak acid solution l)y ferrocfyaiiidc* of
potassium. For this purpose the filtrate, after separating the <*eriinn
group, can be used at once by slightly acidulating with niirie acid, <lilnl-
ing and adding a weak solution of ferrocyanide of ])otaHsium. No pr(‘-
cipitate should appear at once, but by standing for an hour or so some
will come down. Add more ferrocyanide of potassium and rep(‘ai until
the filtrate no longer shows the bands of so-called erbium. AfU^r this
it is best to precipitate with o-xalie acid or oxalate of potassium and
ignite the precipitate so as to get the earth. Dissolve this in nitric? a(*id
and add only water enough to make a very concoutraled syrupy solution.

TiIE Sl?t>AllATJON OP THE EaEE EaETHS

569

Place in a bcal<er at least three inches in diameter and examine with a
spectroscope of low power for absorption bands. Probably the bands of
neodymium and erbiniii will appear. Separate the first by sulphate
of sodium as usnal, and the last by ferroeyanide of potassium from an
acid solution as above. The filtrate will then contain the pure yttrium
(It whose calcined oxalate will ho pure white without trace of yellow.
After separation of iron, calcium, and possibly manganese, the earth will
bo a pure olornont as far as I can tell spectroscopically. However, like
Zv, Fe and many other sul>stances, the ^idclition of Na or E to the elec-
tric arc while obtaining the spectrum will change the intensity of cer-
tain lines of the spectrum, while others are unchanged. If this is con-
sidered as ovidonee of the existence of two elements, then the same evi-
dence will apj)ly to and Zi\ The reason for believing that the sub-
stance thus found is an olemeiit is based on tlie fact that its spectrum
remains unaltered in all minerals and after all chemical operations that
T have been able to dciviso. Furthermore, I believe tliat the new pro-
cess is not only more easy than any other, hut also that it has given a
single element for the first time, as it eliminates the element d. The
yie-ld will of course depend on the amount of purity required. Plom the
earths of gadolinitc about ono-tenth of quite pure yttrium (a) can bo oh-
tainod and about one-twentieth of very pure.

I have determined s])ectroscopically that when, by the ahove process,
the alwoiptioii baud of at last disappears from 3 in. of strong

solution, all the otlier olomonts have also disappeared.

By taking the first prcei])itate several times by ferroeyanide of potas-
sium from an acid solution, a mixture of many elements is obtained
wliicli contains much of that clement to which the so-called ''erbium'*
band is due. By dissolving a weighed quantity of this mixture in nitric
acid and water and examining the band spectnim, I liavo determined the
limit when llie l)an<l can no longer ho se<m. Thus T have proved that
when the band vanishes from 3 inches of concontratod syrupy solution
of yitriiiin there cannot exist in it more than i>or cent of the mixed
elomont as compared with the yttrium, and tliore is prol)ably less.

I have not found foTToeyanido of potassmra useful in the further
stq)aiution of tlie olomemts, hut only in separating out a from the others.

When the neodymiinu Ixind. has (lisapi)carcd by rise of sulphate of
sodium, all the otlier elements of the cerium group have disappeared.
Tlio elomont thorium is sometimes i)roRent in the crude earths, Imt dis-
apjioars after a while irom the purified earths. The conditions for its
disappearance I have not determined.

570

Heney a. Rowland

The elezaents whicli persist to the last hy the ferrocyanide process are
6 aad i, while by Eriiss’ process the element d perasts the longest. As
b-^i has an absorption spectrum and d probably not, the test of purity
by absorption ban& is Tery complete in the new process.

2^ote — For help In tWB investigation xny thanks are dne to a large nnmber of gen-
tlemen. Professor Schapleigh has sent me a large collection of snbstances, Mr.
Hidaen, Professor Wolcott Gibbs, and Professor F. W. Clarke many minerals, Profes-
sor Kriiss several specimens, and Professor Barker and others have helped me in
many vrays.

NOTES OF OBSKEVATION ON THE llONTGEN RAYS

By Henry A. Rowland, N. R. Carmiodabl and L. J. Briggs

lAmerican Jbuimal of Sciefice [4], /, 247, 348, 1836 ; J^Mlofiophical Magaaifie (6], XLT^

881, 383, 1896]

The discovery of Hertz some years since that the catliode rays pene-
trated some opaque bodies like aluminium, has opened up a wonderful
field of research, which has now culminated in the discovery by Eontgen
of still other rays having oven more remarkable properties. We have
confirmed, in many respects, the researches of the latter on these rays,
and have repeated his experiment in photographing through wood,
aluminium, cardboard, hard rubber, and even the larger part of a milli-
meter of sheet copper.

Some of tliese i)hotogra{)hs have been indistinct, indicating a source
of these rays of considerable extent, while others have boon so sharp
and clear cut that the shadow of a coin at the distance of 2 cm. from
the j)hotographic plate has no pemiinbiu whatever, but appears perfectly
sharp even with a low 2 )owor miscroscope.

So far as yet <)l)scrve(l ilu^ rays ])rocoe(l in straight linos and all ollorts
to deflect them by a strong magnet cither within or without the tube
have failed. Likewise i)riBms of wood and vulcanite have no action
what.ev(jr so far as seen, and, contrary to libutgen, no trace of reflection
from a stool mirror at a large angle of incidence could be observed. Tn
this latter experiment the miiTor was on the side of the ])hotographic
plate next to the source of the rays, and not belli n<l it, as in liontgon^s
method.

We have, in the short time we have lieoii at Yvork, principally devoted
ourselves to finding the source ol* the rays. For this puqioso one of
our lubes made for sliowiiig that electricity will not pass through a
vacuum was found to give remarkable results. This lube had the
aluminium jioles willun .1 mm. of each other and had such a perfect
vacuum that sparks gcmcu’ally preferred .10 cm. in air to passage througli
the tube. Jly using potential eriougli, iiowever, the discharge from an
ordinary Ituhmkorfr cioil could lie forced through. The resistance being

572

Henry A. Rowland

so high the discharge was not oscillatory as in ordinary tubes but only
went in one direction.

In this tube we demonstrated conclusively that the main source of
the rays was a minute point on the anode nearest to the cathode. At
times a minute point of light appeared at this point, but not always.

Added to this source the whole of the anode gave out a few rays.
From the cathode no rays whatever came, neither were there any from
the glass of the tube where the cathode rays struck it as Rontgen
thought. This tube as a source of rays far exceeded all our other collec-
tion of Crookes’ tubes and gave the plate a full exposure at 6 or 10 cm.
in about 6 or 10 minutes with a slow-acting coil giving only about 4
sparks per second.

The next most satisfactory tube had aluminium poles with ends about
3 cm. apart. It was not straight, but had three bulbs, the poles being in
the end bulbs and the passage between them being rather wide. In this
case the discharge was slightly oscillatory, but more electricity went one
way than the other. Here the source of rays was two points in the tube,
a little on the cathode side of the narrow parts.

In the other tubes there seemed to be diffuse sources, probably duo
in part to the oscillatory discharge, but in no case did the cathode rays
seem to have anything to do with the Rontgen rays. Judging from tlie
first two most definite tubes the source of the rays seems to bo more
connected with the anode than the cathode, and in both of the tubes the
rays came from where the discharge from the anode expanded itself to-
ward the cathode, if we may roughly use such language.

As to what these rays are it is too early to even guess. That they and
the cathode rays are destined to give us a far deeper insight into nal.ure
nobody can doubt.

Baltimore, Feb. 20, 1896.

NOTES ON EONTGBN RAYS

Br H. A. Bowland, K. B. Cabmiohael akd L. J. Bbiggs
imectrical World, XXVII, 462, 1896]

In the ^ American Journal of Science ^ for March we made a few notes
of oxir researches on the Rontgen rays, reaching the provisional con-
clusion that the main source of the rays was at the anode, and that the
cathode rays seemed to have nothing to do with the phenomena pre-
sented. A further study of the source of the rays in many other tubes
has led ns to modify this conclusion somewhat, for, while we still think
the anode or its equivalent is the main source of the rays, yet we now
have evidence in some of the tubes that it is necessary for the cathode
rays to fall on the anode in order that the Eontgen rays may be formed.

In our tubes with a very high vacuum the other sources of rays are
very faint indeed. We have never obtained any rays from the cathode
e.xeopt in one case, whore undoubtedly there were electrical oscillations
wliicli made the cathode momentarily an anode. It can be readily pro-ved
that these oscillations always exist in the case of lo-w resistance tubes,
and these are probably the cause of many errors in estimating the
source of the rays.

Ill some cases wo have found very faint sources of rays as Eontgen
found them, wlierc the. cathode rays struck the glass, but not where they
struck a piece of platinum kept at nearly zero potential. On the anode
theory, tliis might bo explained by the fact that the bombarding cathode
rays, corning in periodical electrified showers, alternately raise and
lower the potential of the glass, thus making it alternately an anode and
cathode. In the ease of the platinum, this could not occur to the same
extent.

That feeble Eontgen rays emanate from some bodies when bombarded
by the cathode rays, we arc willing to tulmit, and, in fact, had long ago
conic to that conclusion. But we do not agree with Prof. Eliliu Thom-
son’s generaJ conclusion tliat thoHc rays are always given out from bom-
barded surfaces, as we have a tube, with platinum in the focus of a con-
cave electrode, which omits no rays whatever from the platinum, even

674

Henry A. Eov^ land

when the platinum is red hot from the hombardment, the concave elec-
trode being the cathode and a third wire the anode.

The same tube, with the platinum made an anode and the concave
electrode a cathode, produces a profuse radiation of Ebntgen rays in all
directions on the side of the platinum bombarded by the cathode rays,
and none on the other side. In the first case we obtained no rays from
the cathode, no rays from the bombarded surface, and only a very weak
effect from the anode, indeed almost nothing. Hence the condition
for the production of the rays seems to be neither the one or the other
but a combination of the two, and we now believe as far as we can yet
see that the necessary condition for their production is an anode bom-
barded by the cathode discharge. The anode may be, how'ever, an in-
duced anode formed on the glass, and the cathode rays may vary a great
deal and cease to present the usual appearance of cathode rays.

Thus, in the best tube that we have, originally made for showing that
electricity will not pass through a vacuum, the main source is a I'M^int on
the end of the anode, where a little point of light appears. Sometimes,
across the little interval of 1 mm. between the electrodes, a faint spark
or are crosses from one electrode to the other, and we think that the
rays come out especially well under these conditions. Here the action of
the bombarding catliode discharge is rather obscure. This little point of
light also sometimes appears on the red hot platinum anode men-
tioned above, and we have seen it in other tubes, always at the place
where Eontgen rays arc apparently found.

Prof. Blihu Thomson has kindly sent us some sketches of tubes hav-
ing the anode bombarded by the cathode, and we had previously de-
signed some tubes of similar shape, but have not yet found anybody
in this country capable of making a sxifficicntly good vacuum. In many
of our best tubes the vacuum is so perfect as to cause a resistance equal
to a five or six inch spark in the air. The better the vacuum the
greater the number of rays sent out.

However, for sharpness of detail, nothing equals the perfect vacuum
tube, having its electrodes one mm. apart. Such a tube has been de-
signed by one of us, but we have not been able to get the proper
exhaustion.

As to other sources of Eontgen rays, we have tried a torrent of elec-
tric sparks in air, from a large battery, and have obtained none. Of
course, coins laid on or near the plate under these circumstances, pro-
duce impressions, hut these are, of course, induction phenomena.

As to sunlight, Tyndall, Abney, Graham Bell and others, have

NotKS on E5NTGBN RaTS

575

shown that somo of the rays penetrate WQleanite and other opaque
bodies^ and we have only to look at an unpainted door, on the other
side of which the snn is shining, to convince ourselves that sunlight
penetrates wood to a considerable depth.

As to the , theory of the Eontgen rays we know little. If the rays
are vibrations we can readily determine a rough limit to their length,
from the sharpness of the shadows.

Thus onr photographs have such sharpness that the complete waves
cannot be more than -0005 cm. long, but are probably much shorter.
This is independent of whether the waves are longitudinal like sound
or transverse like light, and of course only applies to that portion of
them which affects the photographic plate. There may be others of
larger size that do not affect the plate.

All efforts to bend the rays from their course, either within or with-
out the tube, by means of a strong magnetic field, have failed, both in
our hands and in those of others, and thus, if the rays are radiant parti-
cles of matter, they cannot be highly charged particles like the cathode
rays. The rays are not refracted by any solid bodies so far tried, and
this seems to bo against their being waves either in air or ether. They
])asa through solid bodies, and thus their wave-lengths cannot be very
small. Wc have before seen that it cannot be very great. They cannot
ho sound waves as they proceed for some distance through a very perfect
vticinim.

Altogether we are at a loss for a theory. If we have not yet got a
satisfactory theory of light after more than a hundred years of labor,
how can we hope to have a theory of the Eontgen rays after knowing
of them for only a few months? Let us suspend our judgment for a
while, and let us, above all things, be willing to alter our opinions at
any moment when fresh light appears.

THE RONTGEN RAY, AlTD ITS RELATION TO PHYSICS
(A Topical Discussion)

{.Tramactiom of the American Institute of Electrical Engimers^ Xllly
408 - 410 , 480 , 481 , 1896 ]

Opbning Kbmakkb bt Prop. Henry A. Eowiand

Me. Peesidbnt and Gentlemen: A gentleman aRkcd me a few mo-
ments ago if I knew anything about the X-ray. I told him no; that what
I was going to tell to-night was what I did not know about the X-ray.
I do not suppose anybody can do any more than that, because all of us
know very little about it. We were very much surprised, something
like a year ago, by this very great discoyery. But I cannot say that we
know very much more about it now than we did then. The whole
world seems to have been working on it for all this time without having
discovered very much more with respect to it.

NTow, I suppose it is not necessary for me to go into the history of
the thing. We all know it; how Lonard first, i)robably, discovered those
rays, or discovered something very similar to them; how Eontgen after-
wards found their particular use, their penetrating power, and so on,
although Lenard had found something similar to that before. It is
thus not necessary for me to*go into the history of the matter, but
simply to go over, to some extent, what wo know with regard to these
rays at the present time. First, there was some discussion, some time
ago, as to the source of these rays. Eontgen foimd tliat their source
was any point that the cathode rays struck upon; and you will remember
that when we first knew about those rays they were often called cathode
rays. Many persons tliought that the cathode rays came through the
glass, and Lenard first thought that they did come through his little
window, and it is probable that they do at the present time. Jhit tlxe
kind of rays that we are considering arc very different from tlie cathode
rays. Six months ago there was quite a discussion in regard to the
source, and I believe it was finally determined that they came from
points where the cathode rays strike. At the same time I was rather
opposed to that. In one of my tubes I found that the rays came from

The R6NTGBN- Rat and its Relation to Physios

677

. the anode. I had only the ordinary assortment of Crookes^ tubes, and
one of the tubes had aluminum wires which were a millimeter apart.
In one of these the source of the rays was a point upon the anode —
not upon the cathode at all. It was a very small point. The photo-
graphs which I obtained by that tube were sharper than any I had seen
before. They are so very sharp that in estimating the shadow of an
object I determined that the point could not have been a thousandth
of an inch in diameter. Therefore the source in this case was a very
minute point upon the anode, and that point w^ nearer the cathode,
and I suppose some of the cathode rays might have struck upon it, and
it might have obeyed the law that the point where these X-rays are
formed is the point on the anode where the cathode rays strike.

I had another very interesting tube, and I was going to bring some
of the photographs here to-night; but I thought they were so small that
it would be almost impossible to see them. I tried the three cases in
this tube: First, the case where the cathode rays strike upon the anode.
In that case I got very many Rontgen rays. Then I tried the case
where the cathode rays strike upon an o-bject — a piece of platinum. I
did not get any rays whatever then. How, some people say that they
come from the point where the cathode ray strikes. I did not get any
whatever in that case. In this case the cathode ray struck upon a piece
of platinum in the centre of a bulb, and no rays were given out by the
anode either. Therefore I seemed to have a crucial experiment in each;
I seemed to have the case where the cathode ray strikes upon the anode,
and I got lots of rays. Then I had the case where the cathode rays
strike on a piece of platinum, and I did not get anything at all. Then
where the anode itsdf was free and no cathode rays struck it, I did not
get anything from it. It seemed to me as if the source was most abun-
dant when the cathode ray struck upon the anode; and that is the
theory, we know, upon which nearly all tubes are formed at the present
time. You have the focus tubes in which you focus the cathode rays
upon the anode, and in that case you have a very abundant source of
rays; but I do not believe you ever co-uld get as small a source of rays
as I got with that first tube, where I had a source of a thousandth of an
inch diameter. Having such a small source of rays, it gave me a limit
to the wave-length, if tiiere were waves at all; it would give me a limit
to the wave-length of which I will speak in a moment. As to whether
there are any rays where the cathode rays strike on any other objects,
we know that there are very feeble ones. It seems to be almost neces-
sary in order to get an abundant source that you should have cathode
37

578

Hbnet a. Rowland

rays strike on the anode. However* that is a point of discussion. Now,
BUB to the source of electricity, we have generally the RuhmkorfE coil.
There is oiie source of which I saw a little note in ^ Nature,^ where a
man had used a large Holtz machine with very good, effects. Now it is
very much easier for many persons to use a Holtz machine than to use
a Euhmkorflf coil. There are many cases where one cannot have a large
battery; and this man said that with the Holtz machine he got as great
an effect as with the Euhmkorfl coil. Then we have the Tesla coil, etc.
By the way, speaking of the Tesla coil, I am not sure but that you
might look back and find that it is very similar to the Henry coil.
■Henry originally experimented on the induction of electricity, transmit-
ting a spark of electricity from one coil and getting a spark from an-
other, and the Tesla cod is something like that, except that it is made
so as to produce a much more voluminous spark,

, We all know the properties of the Eontgen rays— they go in a straight
line. Every effort to deviate them from a straight line, by any means
•whatever, has failed, except that when they strike upon an object they
are reflected. Now, it is a question for discussion as to whether there is
^y regular reflection. They strike upon an object, and you get some-
tMng from that object which will affect a photographic plate. Are

those rays which you get from the object Eontgen rays stUl, or do the

Eontgen rays strike upon this object and generate in it some sort of
rays which come out, different from the Eontgen rays, and affect the
plate? We do not know that. Neither are we quite positive whether
there is any reflection of the rays. We know there is turbid reflection —
you may call it— rays strike on the object, and the object becomes a
source of rays of some kind. Nobody has ever found out what sort of
rays come from the object. Something comes from it, and we generally
imagine, and indeed we often state, that they are Eontgen rays that

come off the object. But we have good reason to suppose that they

may be something else; and they may or may not be regular reflections;
some persons say they are and some that they are not. I have seen
some photographs made in this city which indicated regular reflections.
At the same time I would not be positive as to whether there was any
regular reflection. It is rather doubtful. It is a point to be determined.

Then the fluorescence — ^that is the way Eontgen originally found the
ray. You know the way they produce fluorescence — ^the photographic
effect — you all know that. You all know that the magnet does not
affect them— does not turn these rays from a straight line.

The polarization of the rays: We have no evidence whatever as to

The Eontgen Eay and its Relation to Physics 57&

the polarization. If they were very small waves, transverse waves, like
light, we ought to bo able to polarize them. Becq^uerel, by exposing
certain phosphorescent substances to the sun, obtained from them cer-
tain rays which penetrated objects like aluminium, etc. But these rays
were evidently small rays of light, because he could polarize them, and
he could refract them, and they were probably very short waves of ultra
violet light. But we never have been able to discover that there was
any such eifect in a Eontgen ray. Some persons have claimed that they
got polarization; but if there ever was any polarization, it is very small,
indeed. One of the principal advances in respect to these rays is that
made by J. J. Thomson, in considering the electric discharge of bodies.
He has published most valuable results with regard to the effect of
these rays upon gases. When the rays fall upon a gas, they affect the
gas in some way so that it becomes a conductor. !Kro*w, you can subject
the gas to these rays and allow the gas to go through a tube off into
ano-ther vessel, so that it will discharge an electrified body in that vessel.
But he has found the most interesting result that it will not continue
long to affect these bodies. After one has allowed a certain amount
of electricity to pass through it, it then becomes an insulator again.
It only allows a certain amount of electricity to go through it. That is
easily explained — or you can explain it — ^by the Eontgen rays liberating
the ions, and only a certain amount of them. Just as soon as these
are used up in the conduction of the gas, then it ceases to conduct. So
that a certain amount of gas will conduct a certain amount of electricity,
and then it stops conducting. That is a most interesting result. It is
one of the great advances we have made since Eontgen^s discovery.
Eontgen knew nearly all we know now about these rays. We have
discovered very little indeed; but that point I think we have at least
discovered.

Then it is said that these rays afiect a selenite cell in the same way
that light affects it — ^it changes the resistance of the selenite cell.

Of course, we axe only considering the theory to-night; at least I
am, and we do not have to consider the bones, and so on. I have had
some students at work in my laboratory, and it was with the utmost
difficulty that I kept them from photograp£.ing bones. Bones seemed
to be the principal object to be photographed by the Eontgen rays when
they were first discovered, and I suppose it is the same now. Most
people connect Eontgen rays with bones; but I do not intend to say very
much about them.

How, one important point with respect to these rays is as to whether

Hbnbt a. Rowlaitd

.ttey aie homogeneo-oB. Are tbiey like light which can he divided np
into a kige number of different wave-lengths, or are they homogeneous?
There seems to be a great deal of evidence that they are not all the
same; that one ought to get a spectrum of them in some way. Ve can
filter them a little bit through objects. After they are filtered through
an object, they are probably a little different from what they were
before, smd some objects probably let through different rays from others.
In 'Nature ’ Mr. Porter, I believe, has shown experiments upon that. He
divides rays into three kinds. At least he tods that under certain
circumstanceB the rays will penetrate bones better than in other cases—
bones or any other object — ^they have more penetrating power, and they
go through many of those objects that ordinarily stop them. By heat-
ing up the tube, and by various arrangements of his spark-gaps, etc.,
and putting little wires around his tubes, and so on, he can cause them
to generate different kinds of rays. That is a very important point, if
it is substantiated, and there seems to be little reason to doubt that a
number. of rays really do exist; that whatever they are that come from
the object, they are not all the same; some of them penetrate bodies
better than others, and very likely some one will get up some sort of
filter that will filter them out, and allow us to use them and to find if
they have different properties. At the present we are rather in the
dark with regard to this point.

ITow I come to the theory of these rays. What is the cause of all
these phenomena? There was a time when we were rather self-
satisfied, I thick, with regard to theories of light. We thought that
Fresnel and others had discO'Vered what light was— some sort of vibrar
tion in the ether; we called it ether; if it had these waves going through
it, then it would produce light, and we were pretty well convinced that
the waves were transverse, because we would polarize them; so that we
began to be satisfied that we knew something about light. Then Max-
well was horn, and he proved that these rays were electromagnetic —
very nearly proved it. Then Hertz came along and actually showed us
how to experiment with these Maxwell wave^ most of which were
longer than those of light. At the same time they were of the same
nature. Well, we got a rather complicated sort of ether by that time.
The ether had to do lots of things. One must put upon tho ether all the
communication between bodies. For instance, what communication is
there between this earth and the sun? Why, you have light coming
from it and heat. Eadiation you might call it all. We have radiatio-n.
Then some people thought they discovered electromagnetic disturbance

The Eontgbn Rat and its Relation to Physios 581*

froni the sun. Sometimes they have seen a sun spot and noted a defl.ec--
tion of the magnetic needle on the earth. Yery likely that is true. I
don’t know that they have discovered any electrostatic effect. But we
know that electrostatic effects will he carried on through as perfect a
vacuum as you can get. Then we have gravitation action too. Now,
you have got all those things — electromagnetic action, light which
would be an electromagnetic phenomenon, and then we have gravitation,
and we have got to load the ether with all those things. Then we have
got to put matter in the ether and have got to get some connection'
between the matter and the ether. By that time one’s mind is in a
whirl, and we give it up.

Now we have got something worse yet — we have got Rontgen rays on
top of all that. Here is something that goes through the ether, and it
not only goes through the ether but shoots in a straight line right
through a body. Now, what sort of earthly thing can that be? A body
will stop light or do something to it as it goes through;, but what on
earth can it be that goes through matter in a straight line? Why, our
imagination doesn’t give us any chance to do anything with that pro-
blem. It is a most wonderful phenomenon. No-w, we can suppose that
they are ultra violet light. Indeed, we can get a limit to the wave-
length to some extent. Nobody, however, has ever proved that the Ront-
gen rays are waves. But we can get a limit of the wave-length if they ^
waves, because when I have a tube that gives me a shadow which is only
a thousandth of an inch broad, or rather from the greatest intensity
out to clear glass a thousandth of an inch broad, I can calculate the
wave-length of the thing that would produce such a shadow. It has
got to be very small indeed; one knows that right away, because any
ordinary light would make a few waves at the edge of the shadow, and
by mciu^uring tliose waves yoii could get the wave-lengths of the light.
But there was no appearance whatever on any of my photographs of any
such phenomenon as tliat. I did not have any of these waves at the
edge of the shadow whatever. It went directly from blackness to light.
But putting it under the microscope and measuring from almost imag-
inary points, from lightness to darkness, I could get a limit to the wave-
length. Now, as to that limit, I published it in one of the journals
six months ago, or more, and it came at about one-seventh, I think,
that of yellow light. Others have determined the wave-length and got
even below one-seventh that of yellow light. Some have got one-
thirtieth that of yellow light, and so on. Some of them I am rather
doubtful about, because they say they have bands. If they have bands

582

Henry A. Eowland

and diffraction bands, that vould proye instantly that the Rontgen rays
are yrayes. But I have never seen the slightest phenomenon of that
sort. It is very doubtful that it exists, and those persons who have had
it will have to show their photographs very clearly to make us believe
it And therefore we have no evidence whatever that the rays are
waves. At the same time we have no evidence that they are not waves.
They might be very short waves — infinitely short waves. Let us see
what would happen if they were infi.nitely short waves. They might
he so very short as to be too fine-grained for any of our methods of
polarization or reflection. "Waves are reflected from a solid body —
regularly reflected, because they interfere after they come from the
body. You can get the direction — the angle of incidence equals the
angle of reflection; you can get that by means of considering them as
waves and as interfering after they come from the object Well, if the
object however, is a very rough sort of thing co^mpared with the wave-
length, you will not get a regular reflection. That is what might hap-
pen in the case of Rontgen rays. And then again, with regard to
refraction of the light, the theory of refraction which comes from con-
sidering molecules imbedded in the ether will give you some limit.
When we go beyond that limit, we get no refraction. The bending of
the violet rays increases up to a certain point and then goes back. We
haye a case of anomalous refraction very often in some substances like
fuchsine, aniline dyes, and so on. Therefore the action /bf refraction
can he accounted for by having very short waves. But when we treat
of the theory of the case we have the little molecules of a gas knocking
against each other, and they can only go a little distance. We call that
the free path of the gas — a very small distance in the ordinary air.
Those molecules cannot go more than this very small distance before
they stop. Well, now, why should little, short waves of light pass
through the gas and not be stopped too? When the waves are very
short indeed, it seems to me that the object would be entirely opaque
to them, because they would strike upon those molecules, unless they
could pass directly through the molecules. You would therefore neces-
sarily have these little short waves going directly through the mole-
cules, which we generally think is almost impossible iu case of light.
And that is one very great objection that I have to that theory.

Then we have another theory — ^tbat these are not transverse waves
at ail; that they are waves like sound, and very short indeed. Well,
what would happen then? If they axe very short indeed, you have the
same objection: They would aU strike against the molecules, and they

Thb RbNTQBir Eat and its EsDATioir to Phtsios

683

would be dispersed very quickly. The shelter the ■wave-lengths, the
more they axe dispersed. Take, for instance, short ■waves that bob
against a boat and are reflected back. Thus, if you have a big, long
ocean ■wa^ve, it sweeps around a boat and goes on without being troubled
by the boat at all. The shorter the waves, the more they are bothered
by the boat, and so it is -with respect to other waves— the short waves
■would probably be stopped by the molecules. So I do not see what we
can dO’ with regard to it in that respect. According to Matwell’s law,
waves like sound do not exist in the kind of ether that he suggested.
But that is all based upon a certain ■theory ■that the lines of force were
always closed. He introduced into his equation an expression which
indicated that every line of force was a closed pa^th coming back upon
itself or ending in electricity, one or the other. Now, if we throw out
that, then we can get this kind of compressional waves in the ether.
Now, it is not at all impossible that they exist, and as to whether they
would go through molecules any better than light waves do, nobody can
tell; but it is possible that they might. But it there are waves at all,
they must be very short waves. You cannot get over that fact ^if ■they,
are waves at all, they must be short.

Then, of course, you have the other theory — of little particles of
matter flying out from the body, passing through the glass and all other
bodies, until they reach a pliotographic plate or any o-lher place whew
we are no^tified of their presence, and these little particles make their
way through the air or any other substance. Now, why should not the
little particles be stopped very quickly by bodies as well as if the rays
Were waves? You see we are in trouble here too. "Wliy are not the
waves stopped? Why are not the little particles stopped? Stokes has
given some sort of a theory "wi^th regard to this — that, instead of having
a wave motion in the ether, the rays are impulses — a sudden impulse —
one wave, for instance— not a series of waves at aU, but one impulse
coming out from the tube. I think if he had seen any very sharp
shadows obtained from the Ebntgen rays ho would not have givou that
theory. He probably has seen only those very kazy outlines that very
many persons take for Eontgen photographs. But if he had seen any
very defined ones— very sharp ones— he probably would not have given
that theory, because if the Ebntgen rays axe waves at all, they must be
short, and there must be a long series of them to make sharp shadows.
This is why' Newton gave up the wave theoiy of light. You remember
he gave up this theory because he found that light went straight past
an object instead of curving around in^to tbe shadow as much as. sound

684

Hbnrt a. Eowland

does. But he was not quite up to his usual pitch when he made that
statement, because if he had thought a moment he would have seen that
very short waves will go more nearly in a straight lino than long ones.
But any single impulse, such as Stokes suggests, would go into the
^adow. The only wave motion that would go in a straight lino is a
series of waves, one after another. Therefore, these rays cannot bo
single impulses coming irregularly.

Prof. Michelson has suggested a theory of rays based on something
like vortex rings in the ether. » Now, if we have an ether that can carry
on light waves and electromagnetic waves, it cannot be a perfect fluid;
it has got to be something else. You cannot very well imagine vortex
rings in such an ether. So that we are met at every point by some
objection. We have been studying light for hundreds of years; we are
not anywhere near satisfied with the theory yet, and we cannot very
well be expected to be satisfied with the theory of Eontgon rays in one
year.

. Well, I think that is all I can say with regard to the subject, and I
hope the other gentlemen who are to carry on the discussion will satisfy
you on all these points that I have brought up and left unanswered.

[There followed a discixssion by Professor Elihu Thomson, Professor
M. I. Pupiu, and others.]

Peob. Bowulnd: — made a few notes with regard to what has boon
said, but they are made in such a way that I do not believe that I can
interpret them myself, especially as the hour seems to bo getting rather
late. One or two remarks, however, I would like to make. When
Prof. Thomson said that he got such a large amount of rays from an
insulated piece of platinum by letting the cathode rays fall upon it,
he made a sketch. With the exception of this end, which was ilat,
that is the kind of thing that I used. Now, there was abBolut<dy
no effect when this was made an anode and this a cathode, so that all
the cathode rays were striking on the platinum. I have the photo-
graph; I got no effect whatever. Now, if Prof. Thomson got an effect
in this case and I did not get an effect in that case, I have got a case,
at least, where none of these rays were produced by the falling of the
cathode rays upon the object. It doesn’t make any difference how
many other persons have something in which they do get an effect.
If I did not get an effect, that is one case, understand. Tliat is the
ease where the cathode ray fell on an object and I got no Eontgen ray.

The Eonisbit Bay and its Eblatioit xo Phtsios

685

If other people got them in other ways, 'why, there is something else
coming in. I don’t kno'w what it is.

PnoF. Thomson: — I should like to say just there, Professor, if you
would allow me, that I used exactly that arrangement first, and got
rays with the concave cathode. The anode at this end and the inter-
posed plate of platinum between, with that wire extending outward,
is the standard form of Crookes’ tube — the first tube, in fact, that I
used. I got not only sharp effects but rays.

Tbb Chaieman: — ^W as the platinum red?

Pnop. Thomson: — The platinum was red — ^yes, of course, and it was
a vigorous source of rays. I got rap with the same tube that Professor
Bowland does not get them.

Peop. Howland: — ^Well, that has nothing to do with the point. The
point that I raise is this, that there was certainly no doubt that 1 did
not get any, and the cathode rap were falling from the object That
is the thing. ITow, one thing that I wish to remark is that most people
draw a tube like that. They don’t say where the wires go. Mine
generally went out, so that they were very far away from this object.
By curving wires around in different wap I can get an inductive action.
I don’t doubt that I could fix up a tube so that I could get lots of rays
out of any part. However, the time is passing, and I will just say one
word witlr regard to the point Prof. Thomson raised with regard to
the fluoreBcoucc over the surface of the glass. He thought something
was stopped by the glass. I must say that Lonard, when he first experi-
mented upon this subject — ^and I regard his experiments as quite as
valuable as lliintgen’s, probably — he got several kinds of rays coming
out tlirough an aluminium window. He got rays which were deflected
by the magnet, as well as others. He had no't separated them, how-
ever. When the Tjenard paper came to the laboratory I remarked to
my students: “ That is the best discovery that has been made in many
a day.” I immediately set somebody to work experimenting. He tried
to got some results and would probably have discovered the Eontgen
rays at that time if it had not been that the TTniversiiy of Chicago
called him off, and Johns ITopkins University was very poor and could
not eall him back, and he had to stop in the midst of his work. They
always say in Baltimore that no man in that city should die without,
leaving something to Johns Hopkins. How, I)r. Pupin mentioned a.
moans of showing whether tlie rays were reflected — a little reflector in
which he had them brought to a focus, as I recollect it. I have read an
account in which an experimenter did find the rays were brought to a

686 .

Hbnby a. Eowlayd

focTiB, showing, provisionally at least/ that there was some regular reflec-
tion. But these experiments should all be repeated many times before
one aotuaJly believes them. We dotft always believe what we read.

Now, as to Helmholtz’s theory of the motion of ether and so on —
well, as I said before, what is the motion of the ether? What is motion
of the whole ether? Ton cannot move the ether in the whole universe
all at once, and if you do not move the ether in the whole universe
all at once but only move a part, then it is a wave, so it amounts to the
theory that I gave — an impulse, such as Stokes had. Now, an impulse
such as Stokes had does not go in a straight line — ^it goes around cor-
ners — and it does not go in a straight line unless there are lots of
waves coming out. We can readily prove that an ordinary molecule,
vihratiug to ordinary light, must give out a hundred thousand waves
without much diminution of amplitude, or else you cannot have the
sharp lines in the spectrum that we do. The molecule must vibrate a
long time— longer than any bell that we can make. We cannot find a
bell that will give out a hundred thousand vibrations without much
diminution. Tor ethereal waves something must vibrate to produce
them. What it is I don’t know that there is any necessity for discuss-
ing, because you can discuss it forever and never get any nearer to it.
Something vibrates. Now, the thing that vibrates we don’t know. We
don’t know whether it is electricity or whether it is mechanical motion.
We know nothing about it. I have often said to my students, when I
showed them the spectrum of some, substance like uranium, in which
we were taking photographs which would be perhaps ten feet long — so
fine in grain that you could not put the point of a pencil on it without
finding a line. There were thousands of lines. I said to them: “ A
molecule of matter is more complicated a great deal than a piano.
Counting the overtones and everything, you would not probably get up
anywhere near the number of tones you get out of a single molecule of
uranium. Therefore it rather looks as if the uranium molecule was
very complicated.” Of course, all those spectrum lines do not indicate
fundamental tones— many are harmonics. Still it is rather a compli-
cated thing to get a spectrum in which there are many thousands of
lines. So when I come to think what a molecule is and try to get up
some theory of it, I q^uite agree with Dr. Pupin that we don’t know any-
thing about it.

DIFFRACTION GRATINGS

I Kn(iyel^p(Kdif% .Britannka^ Ntw Volumei^ /XT, 458, 459, 19031

The grating is an optical inatrament for the production, of the spec-
trum; it now generally replaces the prism in a spectroscope where large
dispersion is needed, or when the ultra-violet portion of the spectrum
is to be examined, or when the spectrum is to he photographed. The
transpantnt grating consists of a plate of glass covered with lampblack,
gold leaf, opaque collodion or gelatine, the coating being scratched
tlirough in parallel lines ruled as nearly equidistant as possible. When
the lines are to be ruled very close together, a diamond ruling directly
on glass is used. Other transparent materials, such as fluor spar, are
sometimes substituted for glass. For certain researches on long waves
the grating is made by winding a very fine wire, 1-lOOOth inch in diam-
eter, in the threads of two fine screws placed parallel to each other,
soldering the wire to the screws and then eutting it away on one side
of the screws. As the value of a gjrating is dependent upon the number
of linos ruled, it is very desirable to have their number groat. Glass is
so hard that the diamond employed for the ruling wears away rapidly;
and hence the modc»rn grating is generally a reflecting grating, which
is mad(! by ruling on a speculum metal surface finely ground and pol-
ished. oil siudi a surface it is possible to rule 100,000 linos without
damaging the diatnond, although its point oven then often wears away
or breaks down. The lines aro generally so close together as 15,000 or
20,000 i.o the inch, although it is feasible to rule them even olosor—
say 40,000 to 50,000 to the inch. There is little advantage, however,
in the highisr number and many disadvantages.

The grating produces a variety of spectra from a single source of
light, and these aro designated as spectra of the flrst^ second, etc., order,
the nnuiliering commencing from tho central or reflected image and
proceeding in either direction from it. The dispersion depends upon
till! number of linos ruled in a unit of length upon the order of the
spcctruin, and upon the angle at wliich tho grating is held to tho source
of light. Tho defining power depends upon its width and the angles

588

Hbnbt a. Eowlan-d

made liy the mcident and diffracted rays, and is independent of the
number of lines per unit of length ruled on the grating. If this num-
ber is too small, hoveTer, the different order of the spectra will be too
much mired up with each other for easy vision. A convenient number
is 16,000 to 80,000 lines to the inch, or from 6000 to 8000 to the
centimetre. The defining power is defined as the ratio of the wave-
length to the distance apart of the two spectral lines which can be just
seen separate in the instrument. Thus the sodium or J) lines have
wave-lengths which differ from each other by -697 fifx, and their aver-
age wave-length is 689-3 jxfi. A spectroscope to divide them would
thus require a defining power of 988. The most powerful gratings have
defining powers from 100,000 to 800,000. Lord Eayleigh's formula for
-the defining power is

D=Nn.

When D is the defining power, N is the order of the spectrum, and n
is the total number of lines ruled on the grating. As the dA-fini-ng .
power increases -with JT, and since we can observe in a higher order as
the number of lines ruled in a unit of length decreases, it is best to
express the defining power in terms of the width of the grating, iv. In
this case we have for the maximum defining power D' = 80,000 w fox
emaU gra-tings, or 2>' = 15,000 v? for extra fiLne large gratings, w being
the width of the gratings in centimetres. It is seldom that very large
gratings are perfect enough to have a defining power of more than-
10,000 w, owing to imperfection of surface or ruling. The relative
brightness of the different orders of spectra depend upon the shape of
the groove as ruled by the diamond. No two gratings are ever alike
in this respect, but exhibit an infinite variety of distributions of bright-
ness. Copies of glass gratings can be made by photography, contact
prints being taken on eoHodiochloride of silver or other dry plates.
Eeflecting gratings can be copied by pouring collodion or gelatine over
the grating and stripping off the films thus formed. The latter warps,
however, and destroys the definition to a great extent. The grating
always produces a brighter spectrum in the violet than a prism. In
the green the refieeting speculum metal grating may be brighter than
a prism spectroscope of five prisms, and for higher dispersion surpasses
the prism spectroscope both in definition and brightness in all portions
of the spectrum.

To produce the pure spectrum from fiat gratings, two telescopes are
generally used, as in Pig. 1.

Diffbaoxion G-eatings

589

The telescopes are fixed, and the grating is tnmed on its axis to pass
to different portions of the spectrum. As the glass of the telescopes
absorbs the ultra-violet light, this portion of the spectrum is cut off

Fxa. l.— Method of using Flat Grating. Ay source of light; J3, slit; (7,(7, two tel-
escopes, movable or llxed; J>, grating, movable about its centre; By eye-piece.

entirely, unless quartz lenses are used. The concave grating avoids
this trouhlo, and produces a spectrum without the aid of lenses, the
lines being ruled on a concave surface instead of on a flat one. Such a

Fio. 2. —Method of using Concave Grating. Ay source of light; i?, slit; Z), grating
mounted in beam (7, movable along the ways By B] By camera-box or eye-piece.

grating, properly mounted, produces what has been called a normal
spectrum, and is specially adapted to photographic purposes (Pig. 2).

590

Henet a. Eowlaetd

A special form of gratiag of great defining power has been inyented
by Professor Michelson of the TTniTersity of Ohicago^ called the
'echelon' spectroscope (see Speoteosoopt). It isy however, of very
limited application.

See an article on ' Q-ratings in Theory and Practice ’ in Astronomy
and Astro-Physies, XII, p. 129, 1893.

(H. A. E.)

ADDRESSES

A PLEA POE PUEE SCIEE'CE'

ADDRESS AS YIOE-PRBSIDBNT OP SECTION B OF THE AMQBIOAN ASSOOIATION FOE THE
ADVANCEMENT OF SCIENCE, MINNEAPOLIS, MINNESOTA, AUGUST 15, 1888

[Proceedings of iJu American AscociatioTi f<yr ths Advancement of Science^ XXXIX, 106-126,
1883; Science, II, 342-250, 1888; Journal of Franklin Institute, OXYI, 379-399,1888]

The question is sometimes asked us as to the time of year we like
the best. To my mind, the spring is the most delightful; for Nature
then recovers from the apathy of winter, and stirs herself to renewed
life. The leaves grow, and the buds open, with a suggestion of vigor
delightful to behold; and we revel in this ever-renewed life. But this
cannot always last. The leaves reach their limit; the buds open to the
full and pass away. Then we begin to ask omselves whether all this
display has been in vain, or whether it has led to a bountiful harvest.

So this magnificent country of ours has rivalled the vigor of spring
in its growth. I^'orosls have been leveled, and cities built and a large and
powerful nation has been created on the face of the earth. We are proud
of our advancement. We are proud of such cities as this, founded in a
day upon a spot ,ovGr which but a few years since, the red man hunted
the buffalo. But we must remember that this is only the spring of
our country. Our glance must not be backward; for, however beautiful
leaves and blossoms are, and however marvelous their rapid increase,
they are but leaves and blossoms after all. ^ther should we look
forward to discover what will be the outcome of all this and what the
chance of harvest. For if wo do this in time, we may discover the worm
which threatens the ripe fruit, or the barren spot where the harvest is
withering for want of water.

I am required to address the so-called physical section of this asso-

^ In uBinj^ the word “ science,^* I refer to physical science, as I know nothing of
natural science. Probably my remarks will, however, apply to both, but I do not
know.

594

HbNBT a. ROTflAND

ciation. Fain would I Apeak pleasant words to you on this subject;
fain would I recount to yon tke progress made in this subject by my
countrymen, and their noble efforts to understand the order of tlie
universe. But I go out to gather the grain ripe to the harvest, and I
only tares. Here and there a noble head of grain rises above the
weeds; but so few are they, that I find the majority of my countrymen
know them not, but think that they have a waving harvest, while it is
only one of weeds after all. American science is a thing of the future,
and not of the present or past; and the proper course of one in my
position is to consider what must be done to create a science of physics
in this country, rather than to call telegraphs, electric lights, and such
conveniences, by the name of science. I do not wish to underrate the
value of aU these things; the progress of the world depends on them,
and he is to be honored who cultivates them successfully. So also the
cook who invents a new and palatable dish for the table benefits the
world to a certain degree; yet we do not dignify him by the name of a
.^•hoTniBf. Arifl yet it is not an uncommon thing, especially in American
newspapers, to have the applications of science confoiincled with pure
science; and some obscure American who steals the ideas of some great
ryiinfi of the psst, and enriches himself hy the application of tiro same
to domestic uses, is jof ten lauded above the great originator of the id.ca,
who might have worked out hundreds of such applications, had his mind
possessed the necessary element of vulgarity. I have often been asked,
which was the more important to the world, pure or applied science.
To have the applications of a scienee, the science itself must exist.
Should we stop its progress, and attend only to its applications, we
should soon degenerate into a people like the Chinese, who have made
no progress for generations, because they have been satisfied with the
applications of science, and have never sought for reasons in what they
have done. The reasons constitute pure scieucc. They have known
the application of gunpowder for centuries; and yet the reasons for its
peculiar action, if sought in the proper manner, would have developed
the science of ebemistiy, and even of physics, witli all their nuniei’ous
applications. By contenting themselves with the fact that gunpowder
will explode, and seeking no farther, they have fallen hcliind in ilic
progress of the world; and we now regard this oldest and most numerous
of natio-ns as only barbarians, and yet our own country is in this same
state. But we have do^ne better, for wo have taken the science of the
old world, and applied it to all our uses, accepting it like tho rain of
heaven, without nj>kiTi g whence it came, or even acknowledging the

A Plka roK Puke Soibnob

595

tioht of gratitude we owe to the great and nnsclfish workers who have
given it to uk: and, like the rain of heaven, this pure science has fallen
tijKin our country, and made it groat and rich and strong.

'Pet a eivilined nation of the present day, the applications of science
are a nmwity, and our country has hitherto succoeded in this line
only for tlie rotison that there arc certain countries in the world where
pure science haa boon and is cultivated, and whore the study of nature
is »-onsi«lercd a tuililc pursuit; Imt such coxintries are rare, and tluwo who
wish to pursue pure science in «)Hr own country must l>e proi)arod to
fa<H* puhli(! opinion in a manner which rc(iuirc8 much moral courage.
They must be pr(*i«iml to bo looked down upon by every Bucceasful
inventor whos<( shallow mind imngiiu's that tho only pursuit of man-
kind is wealth, and that lut wlio obtains most has host micuocded in this
world. KverylKuiy can i'ompnihend a million of money; but how few
can comprehend any advances in scientific theory, csiM;eially in its more
abstruse (strliotis! And tliis, T iMslieve, is one of the caiises of tho small
number of perstms who have t!V(tr desvoted thc'iuselves to work of tho
higher ord««r in any human pursuit. Man is a gregarious animal, and
dejH'nds veiy much, for his iiap[>inesa, on the symiiaihy of those around
him; and it is rare to find one with tho courage to pursue his own ideas
in sfiitc of his surroundings. In times past, num were more isolated
than at prewuit, and each (!ame in contact with a fewer numlHtr of
poopic. Ilcntsi that lime coiistittites the. period when the great sculj»-
turw, iiaintings and jMicnm w<Te produced, bhuth man’s mind was eom-
I*ara(ivcly free to follow itii own ideals, and the results went the great
and unique works of the ancient masters. 'Po-day tint railrend and tho
telcgmph, the hooks and newspapers, hav(* united each individual man
with the r<'Ht of th(« world; instead of his mind heing an individual, a
thing apart by itself, and unitiue, it has h('(!ome so influenced by tho
outer world, and so <lcpcnd(‘nt upon it, Ihal. it lias lost its originality to
a gr«'nl extent. The man who in times past would nnturally have Imon
in the htwcvl d(fplhs <»r po\crty, mentally and physically, to-day mcas-
nrea Infs* behind a counter, and with lordly air advises the iiaturnlly
Isjrii genius how he may Is'st liring his outward npp<*aranco down to a
level with his own. A new i<Iea he never luul, l»ut li(« c-an at least eover
his menial nakedness wHh ideas imhihed from oUn'rs. Ho tho genius
of the |mst soon pereeives that his Idgher ideas are too high to bo
iippre<>inle<l by the world; his mind is clipped down to tlio standard
form; «'vcry natural oirslutol upwards is ntpressed, until the man is no
higher than his felhiws. llcnce the world, through tho abundance of

596

HBNB.T A. EOWLAND

its iatercouxse, is reduced to a, leveL Wliat was formerly a grand and
magnificent landscape, with, mountains ascending above the clouds, and
depths whose gloom we cannot now appreciate, has become serene and
peaceful. The depths have been filled, and the heights leveUed, and
the wavy harvests and smoky factories cover the landscape.

As far as the average man is concerned, the change is for the better.
The average life of man is fax pleasanter, and his mental condition
better, before. But we miss the vigor imparted by the mountains,
We are tired of mediocrity, the curse of our country; we are tired of
seeing our artists reduced to hirelings, and imploring Congress to protect
t pA-m against foreign competition; we are tired of seeing our country-
men take their science from abroad, and boast that they here convert
it into wealth; we are tired of seeing our professors de^ading their
chairs by the pursuit of applied science instead of pure science, or sit-
ting inactive while tlic whole world is open to investigation; lingering
by the wayside while the problem of the tmiversc remains unsolved. Wo
wish for something higher and nobler in this country of mediocrity, for a
mountain to relievo the landscape of its monotony. We are surrounded
with mysteries, and have been created with minds to enjoy and reason
to aid in the unfolding of such mysterios. Nature calls to us to study
her, and our better feelings urge us in the same direction.

Tor generations there have been some few students of science who
have esteemed tire study of nature the most noble of pursuits. Some
have hcen wealthy, and some poor; but they have all had one thing in
common,— the love of nature and its laws. To these few men the world
owes all the progress duo to applied science, and yet very few ever
received any payment in this world for their labors.

Faraday, the great discoverer of the principle on which all machines
for electric lighting, electric railways, and the transmission of power,
must rest, died a poor man, although others and the whole world have
been ouridied by his discoveries; and such must bo tho fate of the
followers in his footsteps for some time to come.

But there will be those in the future who will study nature from
j)urc love, and for them higher prizes than any yot obtained arc waiting.
We have but yet commenced our pursuit of science, and stand upon the
threshold wondering what there is within. We exjdain the motion of
the planets by the law of gravitation; but who will <'xplivin how two
bodies, millions of miles apart, tend to go toward each other with a
certain force? We now weigh and measure electricity and electric cur-
rents with as much ease as ordinary matter, yet have wo made any

A Plea fob Puee Science

597

approach to an explanation of the phenomenon of electricity? Light is
an Tindnlatory motion, and yet do we know what it is that undulates?
Heat is motion, yet do we know what it is that moves? Ordinary matter
is a common substance, and yet who shall fathom the mystery of its
internal constitution?

There is room for all in the work, and the race has but commenced.
The problems are not to be solved in a moment, but need the best work
of the best minds, for an indefinite time.

Shall our country be contented to stand by, while other countries lead
in the race? Shall wo always grovel in the dust, and pick up the crumbs
which fall from the rich man^s table, considering ourselves richer than
he because we have more crumbs, while we forget that he has the cake,
which is the source of all crumbs? Shall we be swine, to whom the
com and husks are of more value than the pearls? If I read aright the
signs of the times, I think we shall not always be contented with our
inferior position. Prom looking down we have almost become blind,
but may recover. In a new country, the necessities of life must be
attended to fiirst. The curse of Adam is upon us all, and we must earn
our bread.

But it is the mission of applied science to render this easier for the
whole world. There is a story which I once read, which will illustrate
the true position of applied' science in the world. A boy, more fond
of reading than of work, was employed, in the early days of the steam-
engine, to turn the valve at every stroke. ITeccssity was the mother of
invention in his case: his reading was disturbed by his work, and he
soon discovered that he might become free from his work by so tying
the valve to some movable portion of the engine, as to make it move its
own valve. So I consider that the true pursuit of mankind is intellec-
tual. The scientific study of nature in all its branches, of mathematics,
of mankind in its past and present, the pursuit of art, and the cultiva-
tion of all that is great and noble in the world, — ^these are the highest
occupation of mankind. Commerce, the applications of science, the
accumulation of wealth, are necessities which are a curse to those with
high ideals, but a blessing to that portion of the world which has neither
the ability nor the taste for higher pursuits.

As the applications of science multiply, living becomes easier, the
wealth necessary for the purchase of apparatus can be obtained, and
the pursuit of other things besides the necessities of life becomes
possible.

But the moral qualities must also be cultivated in proportion to the

Hbnet a. Eowlaitd

698

•wealth of the cotmtry, before much can be done in pure science. The
successful sculptor or painter naturally attains to wealth through the
legitimate work of his profession. The novelist> the poet, the muaieian,
all ha-ve wealth before them as the end of a successful career. But the
scientist and the mathematician have no such incentive to work: they
must earn their living by other pursuits, usually teaching, and only
devote their surplus time to the true pursuit of their science. And
frequently, by the small salary which they receive, by the lack of instru-
mental and literary facilities, by the mental atmosphere in which they
exist, and, most of all, by their low ideals of life, they arc led to devote
their surplus time to‘ applied science or to o'ther means of increasing
their fortune. How shall we, then, honor the few, the very few, who, in
spite of all difficulties, have kept their eyes fixed on the goal, and have
steadily worked for pure science, giving to the world a most precious
donation, which has home fruit in our greater knowledge of the
universe and in the applications to our physical life which have enriched
thousands and benefited each one of us? There are also those who have
every facility for the pursuit of science, who have an ample salary and
every appliance for work, yet who devote themselves to commercial work,
to testifying in courts of law, and to any other work to increase their
present large income. Such men would be respectable if they gave up
tlie name of professor, and took that of consulting chemist or physicist.
And such men are needed in the community. But for a man to oceupy
the professor’s chair in a prominent college, and, by his energy and
ability in the commercial applications of his science, stand before the
local community as a newspaper cxi)onent of his science, is a disgrace
both to him and his college. It is the death-blow to science in that
region. Call him by his proper name, and he becomes at once a useful
member of the community. Put in liis place a man who shall by pre-
cept and example cultivate his science, and how difleront is the result!
Yonng men, looldng forward into the world for soiuothing to do, see
before them this high and noble life, and they see that there is some-
thing more honorable than the accumulation of wealth. Tlxoy ar(>- thus
led to devote their lives to similar pursuits, and they honor the professor
who has drawn them to something higher than tliuy might otherwise
have aspired to reach.

I do not wish to he misnnderstood in this matter. It is no disgrace
to make money by an invention, or otherwise, or to do commercial
scientific work under some circumstances; but let pure science bo the
aim of those in the chairs of professors, and so prominoirtly the aim that

A Plea foe Puee Soienob 699

there can be no mistake. If onr aim in life is wealth, let us honestly
engage in commercial pursuits, and compete with others for its posses-
sion; but if we choose a life which we consider higher, let us liye up to
it, taking wcaltli or poverty as it may chance to come to us, but letting
neither turn us aside from our pursuit.

The work of teacliing may absorb the energies of many; and, indeed,
this is the excuse given by most for not doing any scientific work. But
there is an old saying, that where there is a will there is a way. Pew
professors do as much teaching or lecturing as the German professors,
who are also noted for their elaborate papers in the scientific Journals.
I myself have been burdened down with work, and know what it is; and
yet I here assert that all can find time for scientific research if they
desire it. But here, again, that curse of our country, mediocrity, is
upon us. Our colleges and universities seldom call for first-class men
of reputation, and I have even heard the trustee of a well-known college
assert that no professor should engage in research because of the time
wasted. I was glad to see, soon after, by the call of a prominent scientist
to that college, that the majority of the trustees did not agree with him,

That teaching is important goes without saying. A successful teacher
is to be respected; but if he does not lead his scholars to that which is
highest, is he not blameworthy? We are, then, to look to the colleges
and universities of the land for most of the work in pure science which
is done. Lot us therefore examine these latter, and see what the pros-
pect is.

One, whom perhaps we may here style a practical follower of Euskin,
has stated that while in this country he was variously designated by the
title of captain, colonel, and professor. The story may or may not be
true, but we all know enough of the customs of our countrymen not to
dispute it on general principles. All men are born equal: some men
title of captain, colonel, and professor. The story may or may not be
The logic is conclusive; and the same kind of logic seems to have been
applied to our schools, colleges, and universities. I have before mo the
report of the commissioner of education for 1880. According to that
report, there were 389,® or say, in round numbers, 400 institutions, calh
ing themselves colleges or universities, in our country I We may well
exclaim that ours is a great country, having more than the whole world
beside. The fact is sufficient. The whole earth could hardly support
such a number of first-class institutions. The curse of mediocrity must

3 864 reported on, and 35 not reported.

600

Henkt a. Eowiand

be upon them, to swarm in. such numbers. They must be a cloud of
mosquitoes instead of eagles as they prof^; and this becomes evident
on further analysis. About one-third aspire to the name of university;
and I note one called by that name which has two professors and
eighteen students, and another having three teachers and twelve stu-
dents! These instances are not unique, for the number of small insti-
tutions and schools which call themselves universities is very great. It
is difficult to decide from the statistics alone the exact standing of these
institutions. The extremes are easy to manage. Who can doubt
that an institution with over eight hundred students, and a faculty of
seventy is of a higher grade than those above cited having ten or twenty
students and two or three in the faculiy? Yet this is not always true;
for I note one institution with over five hundred students which is
known to me personally as of the grade of a high school. Tho statistics
are more or less defective, and it would much weaken tho force of my
remarks if I went too much into detail. I append the following tables,
however, of 330 so-called colleges and universities:

318 had from 0 to 100 students.

88 had from 100 to 300 students.

IS had from SOO to 300 students.

6 had from 300 to 600 students.

6 had over SOO students.

Of 383 so-called colleges and universities:

306 had 0 to 10 in the faculty.

99 had 10 to 80 in the faculty.

17 had 30 or over in the faculty.

If the statistics were forthcoming, — and possibly they may exist, —
we might also get an idea of the standing of these institutions and their
approach to the tnxo university idea, by the average age of the scholars.
Possibly also the ratio of number of scholars to teachers might be of
some help. All these methods give an approximation to tho present
standing of the institutions. But there is auothor method of attacking
the problem, which is very exact, yet it only gives us tho positMlUieii in
the case of the institutions. I refer to the wealth of tho institution.
In estimating the wealth, I have not included the value of grounds and
buildings, for this is of little importance, either to the prosent or future
standing of the institution, as good work can be done in a hovel as in a

A Plea, poe Pueb Soibntob

601

palace. I ha^e taken the productive funds of the institution as the
basis of estimate. I find:

234 have below $500;,000.

8 have between $600,000 and $1,000,000.

8 have over $1,000,000.

There is no fact more firmly established, all over the world, than that
the higher education can never be made to pay for itself. Usually the
cost to a college, of educating a young man, very much exceeds what
he pays for it, and is often three or four times as much. The higher
the education, the greater this proportion will be; and a university of
the highest class should anticipate only a small accession to its income
from the fees of students. Hence the test I have applied must give a
true representation of the possihilities in every case. According to the
figures, only sixteen colleges and universities have $500,000 or over of
invested funds, and o-nly one-half of these have $1,000,000 and over.
Now, even the latter sum is a very small endowment for a college; and
to call any institution a university which has less than $1,000,000 is to
render it absurd in the face of the world. And yet more than 100 of
OUT institutions, many of them very respectable colleges, have abused
the word university in this manner. It is to he hoped that the
endowment of the more respectable of these institutions may be in-
creased, as many of them deserve it; and their unfortunate appellation
has probably boen repented of long since.

But what shall we think of a community that gives the charter of
a university to an institution with a total of $20,000 endowment, two
so-called professors, and eighteen students! or another with three
professors, twelve students, and a total of $27,000 endowment, mostly
invested in buildings! And yet there are very many similar institu-
tions; there being sixteen with three professors or less, and very many
indeed with only four or five.

Such facts as these could only exist in a democratic country, where
])ride is taken in reducing everything to a level. And I may also say,
that it can only exist in the early days of such a democracy; for an
intelligent public will soon perceive that calling a thing by a wrong
name does not change its character, and that truth, above all things,
shoadd be taught to the youth of the nation.

It may be urged, that all these institutions are doing good work in
education; and that many young men are thus taught, who could not
afford to go to a true college or university. But I do not object to the

602

Hbn-et a. Eowland

education, — ^thougli I hare no doubt an investigation would disclose
equal absurdities here, — ^for it is aside from my object. But I do object
to lowering the ideals of the youth of the country- Let them know that
they are attending a school, and not a university; and lot them kno-w
that above them comes the college, and above that the university. Let
them be taught that they are only half educated, and that there are
persons in the world by whose side they arc but atoms. In, other words,
let them be taught the truth.

It may be that some small institutions are of high grade, especially
those which are new; but who can doubt that more than two-thirds of
our institutions calling themselves colleges and universities are un-.
worthy of the name? Each one of these institutions has so-called pro-
fessors, but it is evident that they can be only of the grade of teachers.
Why should they not be so called? The position of teacher is an
honored one, but is not made more honorable by the assumption of a
false title. Furthermore, the multiplication of the title, and the ease
with which it can be obtained, render it scarcely worth striving for.
When the man of energy, ability, and perhaps genius is rewarded by
the same title and emoluments as the commonplace man with the
modicum of knowledge, who takes to teaching, not because of any apti-
tude for his work, but possibly because he has not the energy to com-
pete with his fello-w-men in business, then I say o-ne of the inducements
for the first-class men to become professors is gone.

When work and ability are required for the position, and when the
professor is expected to keep up with the progress of his subject, and
to do all in his power to advance it, and when he is selected for those
reasons, then the position will be worth working for, and the successful
competitor will be honored accordingly. The chivalric spirit which
prompted Faraday to devote his life to- the study of nature may actuate
a few noble men to give their lives to scientidc work; but if we wish to
cultivate this highest class of men in science, we must open a career
for them worthy of their efforts.

Jenny Lind, with her heautiful voice, would have cultivated it to
some extent in her native village; yet who would expect her to travel
over the world, and give concerts for nothing? and how would she have
been able to do so if she had wished? And so the scientific man, what-
ever his natural talents, must have instruments and a library, and a
suitable and respectable salary to live upon, before he is able to exert
himself to his full capacity. This is true of advance in all the higher
departments of human learning, and yet something more is necessary.

A Plea fob Pubb Soibnob

603

It is not those in this coimtrj who receive the largest salary, and have
positions in the richest colleges, who have advanced their subject the
most: men receiving the highest salaries, and occupying the professor^s
chair, are to-day doing absolutely nothing in pure science, but are striv-
ing by the conamercial applications of their science to increase their
already large salary. Such pursuits, as I have said before, are ho-norable
in their proper place; but the duty of a professor is to advance his science,
and to set an example of pure and true devotion to it which shall demon-
strate to his students and the world that there is something high and
noble worth living for. Money-changers are often respectable men, and
yet they were once severely rebuked for carrying on tbeir trade in the
court of the temple.

Wealth does not constitute a university, buildings do not: it is the
men who constitute its faculty, and the students who learn from them.
It is the last and highest step which the mere student takes. He goes
forth into the world, and the height to which he rises has been influenced
by the ideals which he has consciously or unconsciously imbibed in his
university. If the professors under whom he has studied have been
high in their profession, and have themselves had high ideals; if they
have considered the advance of their particular subject their highest
work in life, and are themselves honored for their intellect throughout
the world, — ^the student is drawn toward that which is highest, and
ever after in life has high ideals- But if the student is taught by what
are sometimes called good teachers, and teachers only, who know little
more than the student, and who arc often surpassed and even despised
by him, no one can doubt the lowered tone of his mind. Ho finds that
by his feeble efforts he can surpass one to whom a university has given
its highest honor; and he begins to think that he himself is a horn
genius, and the incentive to work is gone. He is great by the side of
the molehill, and does not know any mountain to compare himself with.

A university should have not only great men in its faculty, hut have
numerous minor professors and assistants of all kinds, and should
encourage the highest work, if for no other reason than to encourage
the student to his highest efforts.

But, assuming that the professor has high ideals, wealth such as only
a large and high university can command is necessary to allow him the
fullest development.

And this is specially so in our science of physics. In the early days
of physics and chemistry, many of the fundamental experiments could
be performed with the simplest apparatus. And so we often find tlie

604

HsiTBy A. Eowi/Aitd

names of 'Wollaston and Faraday mentioned as needing scarcely any-
thing for their researchea Much can even nov he done with tho sim-
plest apparatus, and nohody, except the utterly incompetent, need stop
for want of it; hut the fact remains, that one can only 'be free to invdfeti-
gate in all departments of chenvistiy and physics, when ho not o^nly has
a complete laboratory at his command, hnt a fund to draw on for the
expenses of each experiment. That simplest of the departments of
physics, namely, astronomy, has now reached such perfection that
nohody can expect to do much more in it without a perfectly equipped
ohservatory; and even this would be useless without an income sufideient
to employ a corps of assistants to mate the observations and computa-
tions. But even in this simplest of physical subjects, there is great
misunderstanding. Our country has very many excellent observatories,
and yet little work is done in comparison, because no provision has been
made for maintaining the work of the observatory; and the wealth
which, if concentrated, might have made one effective observatory which
would prove a benefit to astronomical science, when scattered among a
half-dozen merely furnishes telescopes for the people in the surrounding
region to view the moon with. And here I strike the keynote of at least
one need of our country, if she would stand well in science; and the
following item which I clip from a newspaper will illustrate tlxe matter:
" The eccentric old Canadian, Arunah Huntington, who left $200,000
to be divided among the public schools of Vermont, has done something
which will be of little practical value to the schools. Each district will
be entitled to the insignificant sum of $10, which will not advance
much the cause of education.”

Nobody will dispute the folly of sxich a "bequest, or the folly of filling
the country with telescopes to look at the moon, and calling them
observatories. How mu(ri better to concentrate the wealth into a few
parcels, and make first-class observatories and institutions with it!

Is it possible that any of our four hundred colleges and uiiivxirsitieH
have love enough of learning to unite with each other and form larger
institutions? Is it possible that any have such a love of truth that they
are willing to he called hy their right name? I fear not; for tho spirit
of expectation, which is analogous to the spirit of gambling, is strong in
the American breast, and each institution which now, except in name,
slumbers in obscurity, expects in time to bloom out into full prosperity.
Although many of them are under religious influence, where truth is
inculcated, and where men are taught to take a low seat at the tabic
in order that they may be honored by being called up higher, and not

A Plea eoe Pure Soienob

605

dishonored "by being thrust down lo^rer, yet tkese institutions have tbmst
themselves into the highest seats, and cannot prohably he dislodged.

Bnt would it not be possible so to change public opinion that no
college conld be founded with a less endowment than say $1,000,000,
or no university with less than three or four times that amount. Prom
tlio report of tlie commissioner of education, I learn that such a thing
is taking place; that the tendency towards large in.stit’ationB is increas-
ing, and that it is principally in the west and southwest that the naulti-
plication of small institutions with big names is to be feared most, and
that the east is almost ready for the great coming university.

The total wealth of the four hundred colleges and universities iu 1B80
was about $4=0,000,000 in buildings, and $48,000,000 in productive
funds. This would be sujBBcient for one great university of $10,000,000,
four of $5,000,000, and twenty-sir colleges of $^,000,000 each. But
such an idea can of course never be carried out. Govemnaent appro-
priations are out of the question, because no political trickery must be
allowed around the ideal institution.

In the year 1880 the private bequests to all schools and colleges
amounted to about $5,500,000; and, although there was one bequest of
$1,250,000, yet the amount does not appear to be phenomenal It
would thus seem that the total amount was about five million dollars in
one year, of which more than half is given to so-callcd colleges and
universities. It would be very diflB.cult to regulate these bequests so
that they might he concentrated sufficiently to produce an immediate
result. But the figures show that generosity is a prominent feature of
the American people, and that the needs of the country only have to
be appreciated to have the funds forthcoming. Ve must make the
need of research and of pure science felt in the country. We must live
such lives of pure devotion to our science, that all shall see that wo ask
for money, not that we may live in indolent ease at the expense of
charity, but that we may work for that which has advanced and will
advance the world more than any other subject, both, intellectually and
])hy&ically. We must live such lives as to neutralise the influence of
those who in high places have degraded their profession, or harve given
themselves over to ease, and do nothing for the science which they
represent. Let us do what wc can with the present means at our dis-
posal. There is not one of us who is situated in the position best
adapted to bring out all his powers, and to allow him to do most for
his science. All have their difficulties, and I do not think tliat circum-
stances will ever radically change a man. If a man has the instinct of

60S

Henet a. Rowland

reseaicli in him, it will always show itself in some form. But circnm-
stances may direct it into new paths, or may foster it so that what
would otherwise haye died as a bud now blossoms and ripens into the
perfect fmit.

Americans haye shown no lack of invention in small things; and the
same spirit when united to knowledge and love of science, becomes the
spirit of research. The telegraph-operator, with his limited knowledge
of electricity and its laws, naturally turns his attention to the improve-
ment of the only electrical instrument he knows anything about; and his
researches would be confined to the limited sphere of his knowledge,
and to the simple laws with which he is acquainted. But as his knowl-
edge increases, and the field broadens before him, as he studies the
mathematical theo-ry of the subject, and the electromagnetic theo'ry of
light loses the dim haze due to distance, and becomes his constant com-
panion, the telegraph instrument becomes to him a toy, and his efiEort
to discover something new becomes research in pure science.

It is useless to attempt to advance science until one has mastered the
science: he must step to the front before his blows can tell in the
strife. Furthermore, I do not believe anybody can be thorough in any
department of science, without wishing to advance it. In the study of
what is known, in the reading of the scientific journals, and the discus-
sions therein contained of the current scientific questions, one would
obtain an impulse to work; even though it did not before exist; and the
same spirit which prompted him to seek what was already known would
make him wish to know the unknown. And I may say that I neyer met
a case of thorough knowledge in my own science, except in the case of
well-known mvestigators. I have met men who talked well, and I have
sometimes asked myself why they did not do something; but further
knowledge of their character has shown the superficiality of their
knowledge. I am no longer a believer in men who could do something
a they would, or would do something if they had a chance. They are
impostors. If the spirit is there, it will show itself in spite of circum-
stances.

As I remarked before, the investigator in pure science is usually a
professor. He must teach as well as investigate. It is a question which
has been discussed in late years, as to whether these two functions had
better be combined in the same individual, or separated. It seems to
be the opinion of most, that a certain amount of teaching is conducive,
rather than otherwise, to the spirit of research. I myself think that
this is true, and I should myself not like to give up my daily lecture; but

A Plea k)e Pubb Soibnob

607

one must not be oyerburdened. I suppose that the true solution, ia
many cases, would be found in the multiplication of assistants, not only
for work of teaching but of research. Some men are gifted with
more ideas than they can work out with their own hands, and the world
is losing much by not supplying them with extra hands. Life is short:
old age comes quickly, and the amount one pair of hands can do is very
limited. What sort of shop would that be, or what sort of factory, where
one man had to do all the work with his own hands? It is a fact in
nature, which no democracy can change, that men are not equal, — ^that
some have brains, and some hands; and no idle talk about equality can
ever subvert the order of the universe.

I know of no institution in this country where assistants are supplied
to aid directly in research; yet why should it not be so? Even the
absence of assistant professors and assistants of all kinds, to aid in
teaching, is very noticeable, and must be remedied before we can expect
much.

There are many physical prohlems, especially those requiring exact
measurements, which cannot be carried out by one man, and can only
be successfully attacked by the most elaborate apparatus, and with a
full corps of assistants. Such are EegnaulPs experiments on the funda-
mental laws of gases and vapors, made thirty or forty years ago by aid
from the French government, and which are the standards to this day.
Although these experiments were made with a view to the practical
oalcuktion of the steam-engine, yet they were carried out in such a
broad spirit that they have been o-f the greatest theoretical use. Again,
what would astronomy have done without the endowment of observa-
tories? By their means, that science has become the most perfect of
all branches of physics, as it should be from its simplicity. There is no
doubt, in my mind, that similar institutions for other branches of
physics, or, better, to include the whole of physics, would bo equally
succesB&il. A large and perfectly equipped physical laboratory with its
large revenues, its corps of professors and assistants, and its machine-
shop for the construction of new apparatus, would be able to advance
our science quite as much as endowed observatories have advanced
astronomy. But such a laboratory should not he founded rashly. The
value will depend entirely on the physicist at its head, who has to
devise the plan, and to start it into practical working. Such a man will
always he rare, and cannot always he obtained. After one had been
successfully started, others could follow; for imitation requires little
hrains.

608

Hbntrt a, Howland

One coiild not be certain of getting the proper man every time, but
the means of appointment should be most carefully studied so as to
secure a good average. There can be no doubt that the appointment
should rest with a scientific body capable of judging the highest work
of each candidate.

Should any popular element enter, the person chosen would be of the
literary-scientific order, or the dabbler on the outskirts who presents his
small discoveries in the most theatrical manner. What is required is
a man of depth, who has such an insight into physical science that he
can tell when blows will best tell for its advancement.

Such a grand laboratory as I describe does not exist in the world, at
present, for the study of physics. But no trouble has ever been found
in obtaining means to endow astronomical science. Everybody can
appreciate, to some extent, the value of an observatory; as astronomy
is the simplest of scientific subjects, and has very quickly reached a
position where elaborate instruments and costly computations are neces-
sary to further advance. The whole domain of physics is so wide that
workers have hitherto found enough to do. But it cannot always be
so, and the time has even now arrived when such a grand laboratory
should be founded. Shall our country take the lead in this matter, or
shall we wait for foreign countries to go before? They will be built in
the future, but when and how is the question.

Several institutions are now putting up laboratories for physics.
They are mostly for teaching, and we can expect only a comparatively
small amount of work from most of them. But they show progress;
and, if the progress be as quick in this direction as in others, we should
be able to see a great change before the end of our lives.

As stated before, men are influenced by the sympathy of those with
whom they come in contact. It is impossible to change public opinion
in our favor immediately; and, indeed, we must always seek to lead it,
and not be guided by it. For pure science is the pioneer who must not
hover about cities and civilized countries, but must strike into unknown
forests, and climb the hitherto inaccessible mountains which lead to
and command a view of the promised land, — the land which science
promises us in the future; which shall not only flow with milk and
honey, but shall give us a better and more glorious idea of this wonder-
ful universe. We must create a public opinion in our favor, but it need
not at first be the general public. We must be contented to stand aside,
and see the honors of the world for a time given to onr inferiors; and

A Plea foe Pure Soibnoe

609

must be better contented with the approval of our own consciences,
of the very few who are capable of judging our work, than of the whole
world beside. Let us look to the other physicists, not in our own town,
not in our own country, but in the whole world, for the words of praise
which are to encourage us, or the words of blame which are to stimulate
us to renewed effort. For what to us is the praise of the ignorant? Let
us join together in the bonds of our scientific societies, and encourage
each otlier, as we are now doing, in tho pursuit of our favorite study;
kiu)wing that the world, will some time recognize our services, and
knowing, also, that we constitute the most important element in human
progress.

Jhit danger is also near, even in our societies. When the average tone
of tho society is low, when tho highest honors are given to the mediocre,
when third-class men are held up as examples, and when trifiing inven-
tions are magnified into scientific disco-veries^ then the influence o-f
such HocietioK is prejudicial. A young scientist attending the meetings
of siudi a society soon gets perverted ideas. To his mind, a molehill is
a mountain, and the mountain a molehill. Tlie small inventor or the
local celebrity rises to a greater height, in his mind, than the great
leader of science in some foreign land. IIo gauges himself by the
molehill, and is satisfied with his stature; not knowing that he is but
an atom in comparison with the mountain, until, perhaps, in old age,
when it is too late. But, it the size of the mountain had beoti soon at
first, the yemng seiiuitisl would at hnist have b(»on stinuilaled in his
endeavor to grow.

We cannot all be men of genius; but wo can, at least, point them out
to those around us. Wo may not bo able to benefit science much our-
selves; l)ut we can have high ideals on tlie subject, and instil thorn into
those with whom we come in contact. For tlic good of ourselvos, for
tho good of our country, for the good to the world, it is incumbent on
us to form a true estimate of the worth and standing of ])eraonfl and
things, and to set before our own minds all that is great and good and
noble, all that is most important for scientific advance, above the moan
and low and unimporttmt.

It is very often said, that a man hm a right to his opinion. This
might be true for a man oti a desort island, wliosc error would influence
only himself; but when he opens his lips to instruct others, or oven
when he signifies his opinions by his daily life, then ho is directly
responsible for all his errors of judgment or fact. He has no right to
39

610

HBiraT A. Rowiand

fhiTiV a Tn o’iftlii’ll as big as a mountain, nor to teach it, any more than
he has to the "wcxld is flat, and teach that it is so. The facts and
la\fB of our science haTe not eq^ual iinpoitance, neither have the men
who cultivate the science achieved equal results. One thing is greater
than another, and we have no right to neglect the order. Thus shall
our minds be guided aright, and our efforts be toward that which is the
highest.

Then shail we see that no physicist of the first class has ever existed
ia this country, that we must look to other countries for our leaders
in that subject, and that the few excellent workers in our country must
receive many accessions from without before they can constitute an
American sdenoe, or do their share in the world s work.

But let me return to the subject of scientific societies. Here Ameri-
can science has its hardest problem to contend with. There are very
many local societies dignified by high-sounding names, each having its
local celebrity, to whom the privilege of describing some crab with an
extra claw, which he found in his morning ramble, is inestimable. And
there are some academies of science, situated at our scats of learning,
which are doing good work in their localities. But distances arc so
great that it is difficult to collect men together at any one point. "Ere
American Association, which we are now attending, is not a scientific
academy, and does not profess to he more than a gathering of all who
are interested in science, to read papers and enjoy social intercourse.
The National Academy of Sciences contains eminent men from the
whole country, but then it is only for the purpose of advising tbo gov-
ernment freely on scientific matters. It has no building, it has no
library; and it pnbhsbes nothing except the information which ii. freely
gives to the government, which does nothing for it in return. It has
not had much effect directly on American science; hut the libonvlity of
the govemmeut in the way of scientific expeditions, publications, etc.,
is at least partly due to its influence, and in this way it has done imich
good. But it in no way takes the place of the great Eoynl socicsty, or
the great academies of science at Paris, Berlin, Vienna, St. i’otersburg,
Munich, and, indeed, all the European capitals and large cities. These,
hy their publications, give to the yormg student, as well as to the more
advanced physicist, models of all that is considered excellent; and to
become a member is one of the highest honors to which ho can aspire,
while to write a memoir which the academy considers worthy to be pub-
lished in its transactions excites each one to his highest effort.

A Plea k)ii Pubb Soienoe

611

The American Academy of Sciences in Boston is perhaps onr nearest
representation of this class of academies, but its limitation of member-
ship to the state deprives it of a national character.

Blit there is another matter which influences the growth of our
science.

■ As it is necessary for us still to look abroad for our highest inspira-
tion in pure science, and as science is not an affair of one town or one
eoxmlry, but of the whole world, it becomes us all to read the current
journals of science and the great transactions of foreign societies, as well
as those of our own countries. These groat transactions and journals
should be in the library of every institution of learning in the country,
where science is taught. How can teachers and professors be expected
to know what has been discovered in the past, or is being discovered
now, if these arc not provided? Has any institution a right to starve
montally the icaohors whom it omjdoys, or the students who come to it?
There can be but one answer to this; and an institution calling itself a
university, and not having the current scientific journals upon its table
or the transactions of societies upon its library sliolves, is certainly not
doing its best to cultivate all that is best in this world.

Wo call this a free country, and yet it is the only one whore there is a
direct tax upon the pursuit of science. The low state of pure science
in our country may possibly be attributed to the youth of the country;
but a direct tax, to prevent the growth of our country in that subject,
cannot be looked upon as other than a deep disgrace. T refer to the
duty upon fonugn books and periodicals. In our Hcieuccv, no books above
elementary ones have eviu* i)oon published, or are likely to }>e pub-
lished in this (H)uniry; and yet cve^ry tnaclier in physics must have them,
not only in tlie college library, but on his own shelv(‘S, and must ])ay the
govommont of this country to allow him to use a portion of bis small
salary to buy that which is to do good to the whole country. All free-
dom of intercourse which is necessary to foster our growing science is
tliiis brokiui oiT, and that which might, in tiine, rcliiiV(‘ our country of
iis mediocrity, is nij)pcd in the hud by our govcjrnment, which is most
liberal when appealed to diri‘ctly on seienlific suhjeids.

One would think timt hooks in foreign languages might be admitted
free; hut to |)leaHo the half-dozen or so workinon who reprint German
books, not scientific, our free intercourse with that country is cut off.
Our scii(mlifi(i associations and societies must make thomselvos lioard in
this matter, and show ihosc in axitliority how the matter stands.

Hbney a. Rowland

In coBcliisioii, let me say once more that I do not helieTe that our
coimtry is to remain long in its present position. The science of physios,
in -vrliose applications our country glories, is to arise among us, and make
ns respected by tie nations of the world. Such a prophecy may seem
rash with regard to a nation which does not yet do enough physical work
to support a physical journal. But we know the speed with which we
advance in this country: we see cities springing up in a night, and other
wonders performed at an unprecedented rate. And now we see physical
laboratories being built, we see a great demand for thoroughly trained
physicists, who have not shirked their mathematics, both as professors
and in so-called practical life; and perhaps we have the feeling, common
to all trae Americans, that our country is going forward to a glorious
future, when we shall lead the world in the strife for intellectual prizes
as we now do in the strife for wealth.

But if this is to be so, we must not aim low. The problems of the
universe cannot be solved without labor; they cannot be attacked with-
out the proper intellectual as well as physical tools; and no physicist
need expect to go far without his mathematics. No one expects a horse
to win in a great and long race whd has not been properly trained; and
it would be folly to attempt to win with one, however pure his blood
and high his pedigree, without it. The problems we solve are more diffi-
cult than any race; the highest intellect cannot hope to succeed without
proper preparation. The great prizes are reserved for the greatest
efforts of the greatest intellects, who have kept their mental eye bright
nnil fle sh hard by constant exercise. Apparatus can be bought with
money, talents may come to us at birth; but our mental tools, our mathe-
matics, our experimental ability, our knowledge of what others have
done before us, all have to be obtained by work. The time is almost
past, even in our own country, when third-rate men can find a place as
teachers, because they are unfit for everything else. Ve wish to see
brains and learning, eombined with energy and immense working
power, in the professor’s chair; but, above all, we wish to see that high
and chivalrous spirit which causes one to pursue his idea in spite of all
difficulties, to work at the problems of nature with the approval of his
own conscience, and not of men before him. Let him fit himself for
the struggle with all the weapons which mathematics and the experi-
ence of those gone before him can furnish, and let him enter the arena
with the fixed and stem purpose to conquer. Let him not he contented
to stand hack with the crowd of mediocrity, but let him press forward
for a front place in the strife.

A PlBA JOB PlTBB SOIBNOB

613

The whole TmiTeree is before ns to study. The greatest labor of the
greatest minds has only giyen us a few pearls; and yet the limitless
ocean, with its hidden depths jBlled with diamonds and precious stones,
is before us. The problem of the universe is yet unsolved, and the mys-
tery involved in one single atom yet eludes us. The field of research
only opens wider and wider as we advance, and our minds are lost in
wonder and astonishment at the grandeur and beauty unfolded before
us. Shall we help in this grand work, or not? Shall our country do
its share, or shall it still live in the almshouse of the world?

THE PHTSICAL LABORATOEY IN MODERN EDUCATION

ABDRBBB TOR OOMMRHOBATION DAT OT THB JOllllS HOPKINB UNIVBliBlTY,
TBBBUABT 22, 1886

iTchm Hopkins ‘University Circulars^ No. 50, pp. lOJJ-105, 1880]

Prom the moment \7e are born into this world down to the day whou
we leave it, we are called upon every moment to exorcise our judgment
with respect to matters pertaining to our welfare. While nature has
supplied us with instincts which take the place of reason in our infancy.,
and which form the basis of action in very many persons through life,
yet, more and more as the world progresses and as we depart from the
age of childhood, we are forced to discriminate between right and wrong,
between truth and falsehood. ITo longer can we shelter ourselves behind
those in authority over us, but we must come to the front and each oiu^
decide for himself what to believe and how to act in the daily routine
and the emergencies of life. This is not given to us as a duty whic.li wo
can neglect if we please, but it is that which every man or woman, con-
.sciously ox unconsciously, must go through with.

Most persons cut this Gordian knot, which they cannot untangle, l)y
accepting the opinions which have been taught them and which appear
correct to their particular circle of friends and asRociatoH: others take
the opposite extreme and, with intellectual an’ogancc, seek to build up
their opinions and beliefs from the very foundation, individually and
alone, without help from others. Intermediate between those two ex-
tremes comes the man with Ml respect for the opinions of tliosc around
him, and yet with such discrimination that ho sees a chance of error
in all and most of all in himself. He has a longing for tlie truth and is
willing to test himself, to test others and to test nature until he Ihids it.
He has the courage of his opinions when thus carefully formed, and
is then, but not till then, willing to stand before the world and proclaim
what he considers the truth. Like Galileo and Copernicus, he inaugu-
rates a new era in science, or like Luther, in the religious belief oE man-
kind. He neither shrinks within himself at the thought of having an
opinion of his own, nor yet believes it to be the only one worth consid-
ering in the world; he is neither crushed with intellectual humility, nor
yet exalted with intellectual pride; he sees that tlio problems of nature
and society can be solved, and yet he knows that this can only come

The Physical Laboratoey in Modern Education 615

about by tbe combined intellect of the world acting through ages of time
and that he, though his intellect were that of Newton, can, at best, do
very little toward it. Knowing this he seeks all the aids in his power
to ascertain the truth, and if he, through either ambition or loye of
truth, wishes to impress his opinions on the world, he first takes care
to haye them correct. Aboye all, he is willing to abstain from haying
opinions on subjects of which he knows nothing.

It IS the proyince of modern education to form such a mind while at
the same time giying to it enough knowledge to haye a broad outlook
oyer the world of science, art and letters. Time will not permit me to
discuss the subject of education in general, and, indeed, I would be
transgresKing the principles above laid down if I should attempt it. I
shall only call attention at this present time to the place of the labo-
ratory in modern education. I haye often had a great desire to know
the state of mind of the more eminent of mankind before modern science
changed the world to its present condition and exercised its influence
on all departments of knowledge and speculation. But I have failed
to picture to myself clearly such a mind while, at the same time, the
study of human nature, as it exists at present, shows me much that I
suppose to be in common with it. As far as I can see, the unscientiflc
mind differs from the scientific in this, that it is willing to accept and
make statements of which it has no clear conception to begin with and
of whose truth it is not assured. It is an irresponsible state of mind
without clearness of conception, where the connection between the
thought and its object is of the yaguest description. It is the state of
mind where opinions are given and accepted without ever being sub-
jected to rigid tests, and it may have some connection with that state of
mind where everything has a personal aspect and we are guided by
feelings rather than reason.

When, by education, we attempt to correct these faults, it is neces-
sary that we have some standard of absolute truth: that we bring the
mind in direct contact with it and let it be convinced of its errors again
and again. Wo may state, like the philosophers who lived before Gali-
leo, that large bodies fall faster than small ones, but when we see them
strike the ground together we know that our previous opinion was false
and wc learn that even the intellect of an Aristotle may he mistaken.
Thus we are taught care in the formation of our opinions and find that
tlie unguided human mind goes astray almost without fail. We must
correct it constantly and convince it of error over and over again until
it discovers the proper method of reasoning, which will surely accord
with the truth in whatever conclusions it may reach. There is, however.

616

Hbnbt a. Eo'wxand

danger in this process that the mind may become orer cautious and thus
present a •weakness when brought in contact "with an unscrupulous per-
son who cares little for truth and a great deal for effect. But if we
believe in the maxim that truth -will prevail and consider it the duty
of ah educated men to aid its progress, the kind of mind which I describe
is the proper one to foster by education. Let the student bo brought
face to face •with nature: let him exercise his reason with respect to the
simplest physical phenomenon and then, in the laboratory, put hie opin-
ions to the test; the result is invariably humility, for he finds •that nature
has laws which must be discovered by laboir and toil and not by wild
fights of the imagination and scintillations of so-caUed genius.

Those who have studied the present state of education in the schools
and colleges tell us that most subjects, including the sciences, are taught
as an exercise to the memory. I myself have witnessed the melancholy
sight in a fashionable school for young ladies of those who were bom
to be intellectual beings reciting page after page from memory, -without
any effort being made to discover whether they understood the subject
or not. There are even many schools, so-called, where the subjec-t of
physics or natural philosophy itself is taught, without even a class ex-
periment to illustrate the subject and connect the words -with ideas.
Words, mere words, are taught and a state of mind far different from
that above described is produced. If one were required to find a sys-
tem of education which would the most surely and certainly disgust the
student -with any subject, I can conceive of none which would do this
more quickly than this method, where he is forced to learn what he
does not understand. It is said of the Faraday that he never could
understand any scientific experiment thorougily until he had not only
seen it performed by others, but had performed it himself. Shall we
then expect children and youth to do what Faraday could not do? A
thousand times better never teach the subject at all.

Tastes differ, but we may safely say that every subject of study which
is thoroughly understood is a pleasure to the student. The healthy
mind as well as the healthy body craves exercise, and the school room
or the lecture room should he a source of positive enjoyment to those
who enter it. Above all. the study of nature, from the magnificent uni-
verse, across which light itself, at the rate of 186,000 miles per second,
cannot go in less than hundreds of years, down to the ato^m of which
millions are required to build up the smallest microscopic object, should
be the most interesting subject brought to the notice of the student.

Some are horn blind to the beauties of the world around them, some

The Phtbical Laboratoex in Modern Ei)u6ation 617

haye their tastes better developed in other directions, and some have
minds incapable of ever understanding the simplest natural phenomenon;
but there is also a large class of students who have at least ordinary pow-
ers and ordinary tastes for scientific pursuits: to train the powers of
observation and classification let them study natural history, not only
from books, but from prepared specimens or directly from nature: to
give care in experiment and convince them that nature forgives no
error, let them enter the chemical laboratory: to train them in exact and
logical powers of reasoning, let them study mathematics: hut to com^
bine all this training in one and exhibit to their minds the most perfect
and systematic method of discovering the exact laws of nature, let them
study physics and astronomy, where observation, common sense and
mathematics go hand in hand. The object of education is not only to
produce a man who Jcnows, but one who ioesj who makes his mark in
the struggle of life and succeeds well in whatever he undertakes: who
can solve the problems of nature and of humanity as they arise, and who,
when he knows he is right, can boldly convince the world of the fact.
Mon of action are needed as well as men of thought.

There is no doubt in my mind that this is the point in which much
of our modem education fails. Why is it? I answer that the memory
alone is trained and the reason and judgment are used merely to refer
matters to some authority who is considered final, and worse than all,
they are not trained to apply their knowledge constantly. To produce
men of action they must he trained in action. If the languages be
studied, they must be made to translate from one language to the other
until they have perfect facility in the process. If mathematics be
studied, they must work problems, more problems and problems again,
until they have the use of what they know. If they study the sciences,
they must enter the laboratory and stand face to face with nature; they
must learn to test their knowledge constantly and thus see for them-
selves the sad results of vague speculation; they must leam by direct
experiment that there is such a thing in the world as truth and that
their own, mind is most liable to error. They must try experiment after
experiment and work problem after problem until they become men of
action and not of theory.

This, then, is the use of the laboratory in general education, to train
the mind in right modes of thought by constantly bringing it in con-
tact with absolute truth and to give it a pleasant and profitable method
of exercise which will call all its powers of reason and imagination into
play. Its use in the special training of scientists needs no remark, for it

618

Henry A. Eowland

is well known that it is absolutely essential. The only question is
whether the education of specialists in science is worth undertaking at
all,, and of these I have only to consider natural philosophers or physi-
cists. I might point to the world around me, to the steam engine, to
labor-saving machinery, to the telegraph, to all those inventions which
make the present age the ''Age of Electricity,” and let that be my
answer. Hobody could gainsay that the answer would be complete, for
all are benefited by these applications of science, and he would be con-
sidered absurd who did not recognize their value. These follow in the
train of physics, but they are not physics; the cultivation of physics
brings them and always will bring them, for the selfishness of mankincl
can always be relied upon to turn all things to profit. But in the edu-
cation pertaining to a university we look for other results. The special
physicist trained there must be taught to cultivate his science for its
own sake. He must go forth into the world with enthusiasm for it and
try to draw others into an appreciation of it, doing his part to convince
the world that the study of nature is one of the most noble of pursuits,
that there are other things worthy of the attention of mankind besides
the pursuit of wealth. He must push forward and do what he can, ac-
cording to his ability, to further -the progress of his science.

Thus does the university, from its physical laboratory, send forth into
the world the trained physicist to advance his science and to carry to
other colleges and technical schools his enthusiasm and knowledge.
Thus the whole country is educated in the subject and others are taught
to devote their lives to its pursuit, while some make the applications to
the ordinary pursuits of life that are appreciated by all.

But for myself, I value in a scientific mind most of all that love of
truth, that care in its pursuit and that humility of mind which makes
the possibility of error always present more than any other quality. This
is the mind which has built up modem science to its present perfection,
which has laid one stone upon the other with such care that it to-day
offers to the world the most complete monument to human reason. This
is the mind which is destined to govern the world in the future and to
solve problems pertaining to politics and humanity as well as to inani-
mate nature.

It is the only mind which appreciates the imperfections of the human
reason and is thus careful to guard against them. It is the only iiiiiid
that values the truth as it should be valued and ignores all personal
feeling in its pursuit. And this is the mind the physical laboratory is
built to cultivate.

ADDRESS AS PRESIDESTT OF THE ELECTRICAL OONFBE-
ENOB AT PHILADELPHIA, SEPTEMBER 8, 1884

{Beport of the Conference^ pp. 13-38, Washington, 1886]

To the student of science who has a disposition to look into the pages
of history, no life has greater interest than that of Archimedes, and yet
there are few men about whom so little is known. Living more than
two thousand years ago, the accounts of him which have come to us are
little short of fabulous, and yet they axe of such a nature that we can
say without any doubt that he was a genius such as the world has sel-
dom seen. To him we owe some of the fundamental facts of mechanics,
such as the principle of the lever and the pulley, and the fact that a
body immersed in a liquid loses in weight as much as an equal volume
of the liquid weighs. And in military engineering his success was so
great that he prolonged the siege of Syracuse by the Eomans from what
would probably have been a few days to three years. His engines shot
against the enemy immense numbers of darts and huge stones, which
mowed them down in columns, and falling on their ships destroyed
them. He thrust out huge beams from the walls over the ships and
drew them into the air, where they swung to and fro to the amazement
and terror of the Eomans and were finally dropped and sunk to the bot-
tom of the sea. He is even said to have set them on fire by means of
the reflected light of the sun. But his principal work was in geometry,
and of this I only need to quote the words of Professor Do Morgan re-
ferring to those geometrical works of Archimedes which have come
down to us. Here,” says Professor De Morgan, he finds all that re-
lates to the surface and solidity of the sphere, cone and cylinder and
their segments. A modem work on the differential calculus would not
give more results than are found here.’^ As to the quality of the indi-
vidual, the impression which his writings give us is that of a power
which has never been surpassed. No one has a right to say tliat New-
ton himself, in the place of Archimedes, could have done more.

Thus before the birth of modorn science, in the dim ages of the past
when the light of history begins to fade and the mist of legend to cover

620

Henry A. Eowland

OUT Tie'w, there lived a man of almost superhuman intellect whose mind
seemed equally adapted to either pure or applied science. And yet Plu-
tarch says of him: ^^Archimedes possessed so high a spirit, so profound
a soul, and such treasures of scientijBc knowledge, that, though the in-
ventions (referring to his military engines) had now obtained for him
the renown of more than human sagacity, he yet would not deign' to
leave behind him any commentary or writing on such subjects, but, re-
pudiating as sordid and ignoble the whole trade of engineering, and
every sort of art that lends itself to mere use and profit, he placed his
whole affection and ambition in those purer speculations where there
can be no reference to the vulgar needs of life; studies, the superiority
of which to all others is unquestioned, and in which the only doubt can
be, whether the beauty and grandeur of the subjects examined, or the
precision and cogency of the methods and means of proof, most deserve
our admiration.”

Here, then, at the dawn of science the question of the relative value
of pure and applied science had been brought up! To the people of
Syracuse, who had to defend themselves against an overwhelming enemy,
the military engines of Archimedes were of far more interest than the
whole of geometry, for the knowledge of the ratio of the solid contents
of a sphere and its circumscribed cylinder cannot bring a dead man to
life or restore wealth to a plundered city. And yet, from a point of
view distant more than two thousand years, we are forced to admit that
Archimedes was right. Archimedes’ engines of destruction have passed
away, but the geometrical and mechanical truths which he discovered
are to-day almost the axioms of the mathematician and the worker in
physical science, and the ratio of the circumference of a circle to its
radius is to-day the most important of our physical constants.

But this is only a meager part of the influence of this raan. The
truths which he discovered have formed a part of the education of every
student of mathematics to the present time, and have given pure intel-
lectual enjoyment to all. They have helped to form the minds of all
those whom we consider great in our scieuce, and they have done their
share in that march of progress which is gradually trausforniing the
world.

Great should be the honor in which we hold the intellect of Archime-
des, but greater should be our reverence when we approach that noble
spirit which could ignore all worldly considerations and prefer the truths
of geometry to the vast physical power given him by his other inven-
tions, which were his amusements for a moment. We now see that he

EIiBOTEIOAL CONI'HKEirOE AT PHILADELPHIA

621

vas right, "btit we cannot for a moment suppose that he foresaw, except
dimly, any so-called practical adyantages from his discoveries. A thou-
sand times no! He preferred his geometrical labors because of a subtle
quality of his mind, an instinct toward that which was highest and
noblest and a faith that the pursuit of what is noble is the surest road
to the final happiness of the indiyidual and of the world. Our highest
moral qualities are of this nature, and we despise as the lowest of the
low one who is honest because ^^honesty is the best policy, but esteem
him whose instincts lead him to honesty whatever the consequences.

So we reverence the noble and lofty spirit of Archimedes, and yet we
do not at the present day quite agree with his estimate of the relative
value of his works. His military inventions were far from worthy of
being despised, even though the only reason were that they gave the
world three more years of Archimedes^ life. The world is not formed
of disembodied spirits, but of men, in whom there is a wonderful com-
bination of mind and matter, and a sound mind in a sound body; is the
highest type of manhood. But we also know that the mind is hampered
by many considerations connected with the body. Archimedes recog-
nized this, and his noble spirit revolted at it But to-day we see that
no progress can come from this method of treatment; the body still re-
mains, however much we may despise it, and the buzzing of a fly can
disturb the most profound thought of the philosopher.

We now study the laws of nature and seek thus to assist our bodies
in obeying the thoughts of our minds. Our railroads carry us hither
and thither on the earth with somewhat the facility of spirits, and our
thoughts pass with almost the speed of light to the uttermost portio-n
of the earth. THhie steam engine does our work, and labor-saving ma-
chinery takes the place of our hands. With a minimum amount of labor
we can to-day possess luxuries unknown even to kings in ancient times,
and our minds are free to study the order of nature or engage in any
intellectnal pursuit we may desire. Instead of being the slaves of na-
ture and groveling in the dust before her to find the food which wo
crave, we have now assumed the command, and find her a willing servant
to those who Icnow her language.

But here we reach the keystone of the problem. To command her we
must know her language. Knowledge, then, is the price of her service,
and she obeys not the ignorant or degraded, but grinds them into dust
beneath her heel.

Elnowledge, then, is power, and it is more than powers it is that
which the intellect most craves and is the object of many of our highest

Hbnst a. Rowland

aspirations. What truth is, is the goal of intellectual mankind in all
ages, and its pursuit leads not only to intellectual hut also to physical
satisfaction.

The pursTiit of the one leads to the other, and we shall see as we pro-
ceed that the only way for the world to progress in practical scioneo is
by the cultiyation of the theoretical science.

Pure science must exist before its applications, and the truths of pure
science are far more reaching in their effects than any of its applica-
tions; and yet the applications of science often have a much more im-
mediate interest for the world at large than many discoveries in pure
science, which will finally revolutionize it, both physically and mentally.
They both have their importance and both are at work in causing that
intellectual and material progress in which the world is now ])ushing
forward with giant steps. But there is this difference — ^the names of the
great inventors are seen in every paper and their deeds are recounted
to the rising youth of the country as examples to be followed. And
yet the discoveries of the principles on which their inventions are based
may have died in comparative obscurity, with poverty knocking at the
door. We are in no danger of forgetting those who have been success-
ful in those applications of science which are in daily use, and it is use-
less to repeat the story of the telegraph or telephone, but it will be of
more interest for me to recall to your minds a few of the landmarks iu
our science and then to consider the present state of our science, with
a possible glance into the future.

Thus we sk«n obtain a clearer view of how our science has boon built
up and of the means which are necessary for its furtlun progress. Wo
aTinll also See the relations between pure and applied scionco, and the
relative importance of the two in the progress of the world.

It is impossible for one here to discuss the reasons why the nucionts
followed their science to so short a distance and tlio world had to wait
more than two thousand years before the light of unxli’m stdoiuH* com-
menced to shine. It must he left to the psychologisis and historians.
But this I may say, modem progress is entmdative. By Iho study of
the science of the past, the minds of mon arc trained for its further ad-
vance in the future, and so when there was no seioneti to study there
could be but little training of the mind in tlio Irue methods of Ihonghl.

The average intellect of mankind has improvcid, and what, (tould only
have been comprehended in past times by a few is to-day nnder8t«)<.)d
by the majority of educated persons. And this iiKe-ease has Ix'CiU most
apparent in the reason and moral sense of urnnkind, the two (lualitics of

Eleotkioal Conferbnoe at Philadelphia

6^3

the mind which come most into play in the stndy of science. To the
mind of the ancients, where the imagination ran riot without the guide
of reason or a warning from their moral sense to speah the truth, it was
easier to attribute the attraction of rubbed amber to an inherent soul
or essence, which, awakened by friction, went forth and brought back
the small particles floating around, than to examine and find out the
truth.

The simple experiment of the amber remained .without investigation
for 2800 years. Had the reasoning of many modem persons been fol-
lowed, we should never have had a science of electricity. Why should
anybody investigate this phenomenon, this feeble force, which could
only attract a few particles of dust? The world could cat, drink, and
take its ease without doing anything in the matter, and it did so for
more than two thousand years of intellectual, moral and physical degra-
dation. Then the awakening came, and men began to feel that they
were reasoning beings. They began to see that there were other pleas-
ures in the world besides animal pleasures, and that they had been placed
in this wonderful universe that they might exalt their intelligence by its
proper study. Ho question of gain entered into the minds of these
early investigators, but they were led by that instinct toward truth which
indicates the highest type of man. And yet their rcsoarclics have traus-
formcd the world, not only intellectually, but physically. Some would
say that science had been degraded by its applications, but who that
looks over the world at the present time can think so? There is no
danger of this view becoming general; the danger is in the other
direction, and that science shall be degraded in the estimate of the
world by the idea that its principal use is to be applied to the common
purposes of life. A thousand times no! Its uso is in the intellectual
training of mankind and the high and noble pleasure it gives to those
who are bom to understand it; to lift mankind above tlic level of the
brute and to make him appreciate the beauties and wonders of nature;
to cause him to stand in humiliation and awe beforo that universe
which the intellect of ages has attempted to understand and yot has
failed; to make even Newton say, know not what the world may
think of my labors, but to myself it seems to me that I have been but
as a child playing on the soasliore; now finding some i)ebl)le rather more
polished, and now some shell rather more agreeably variegated than
another, while the immense ocean of truth extended itself unexplored
before me.”

But the great moral law of the universe here enters. If the world

624

Hbney a. Bowland

would only pursue those things which are high and right and noble its
reward would not be confined to the minds of men. Physical rewai-d.s
await it as well, and disease, that principal . cause of human misex^y^
would almost pass away when the effect of inheritance from the present
generation had passed. So the pursuit of pure science brings not only
the rewards I have mentioned, but the physical rewairds of applied
science and the pursuit of applied science gives wealth which may TDe
again employed to further pure science. So the two react on each otlxeir
to produce that perfect whole, modem science, pure and applied.

This moral law of the universe is well illustrated by the well-known
story of Solomon:

" The Lord appeared to Solomon in a dream by night; and God said.
Ask what I shall give thee.

^‘^And Solomon said. Thou hast made thy servant king instead of David
my father, and I am but a little child; I know not how to go out or come
in. Give therefore thy servant an understanding heart to judge thy
people, that I may discern between good and bad; for who is able to
judge this thy so great a people?

"And God said unto him. Because thou hast asked this thing, and hias-b
not asked for thyself long life, neither hast asked riches for thyself, ixor-
hast asked the life of thine enemies, but hast asked for thyself under-
standing to discern judgment, behold, I have done according to thy
words; lo, I have given thee a wise and an understanding heart, so that
there was none like thee before thee, neither after thee shall any arise
like unto thee. And I have also given thee that which thou hast ixot
asked, both riches and honor; so that there shall not be any among the
kings like unto thee all thy days.^^

So the world, when it chose knowledge and truth above all things,
acquired not only the treasures of pure theoretical science, but also the
wealth and riches and honor which come from applied science such, as
the world has never seen before and could see in no other way.

It is to William Gilbert, an English physician, that we owe the com-
mencement of the modern science of electricity. His book on the mag-
net was published in 1600, and contained his electrical experiments.
Thus, at this early date, the similarity of electrical to magnetic attrac-
tion was recognized. But how slowly did the subject advance! The
difference between conductors and non-conductors was discovered *by
Gray. But not until 1?'46, 150 years after Gilbert, was the Leyden 3 ax-
invented. Then the remarkable nature of the phenomenon became ap-
parent, and the world was startled by it. The subtle spirit which wexi*fc

Elboteioal Confbebnob at Philadelphia

626

forth from the amber, -which was so feeble as only to attract dust, now
flashed forth with light and sound and heat, and could cause the strength
of the giant to vanish. To the world at large there was now something
worth looking into. But do we think that the spark from the Leyden
jar is more wonderful tliaii the gentle attraotion of the aml>er? By no
means, for, to the scientist, they are both equally remarkable, and be-
yond our powers of explanation. It is only to the vulgar and unedu-
cated taste that the tinsel and gewgaws of an electric spark appeal more
strongly than the subtle spirit of the amber. Nevertheless, despicable
as the means, the spark of the Leyden jar acted as a trumpet call to
Europe and even America to come to the study of the wonderful science
of electricity. At no other time has there been such excitement over
any electrical discovery, and electrical experiments became general.

It was only after the discovery of the Leyden jar that the idea of an
electric current occurred to mankind, and this current was even trans-
mitted to a distance by a wire and a shock given to a person across the
Thames, the water forming the return circuit. And the English ex-
perimenters even went so far as to form a circuit with the two observ-
ers two miles apart, using the earth as the return circuit. Thus the
fundamental fact which forms the basis of the telegraph -was early ob-
served.

But isolated facts are of little .value unless connected together by
something which we call a theory, and in this line we owe much to
Eranklin, whoso letters upon this subject appeared between 1747 and
1764. To him we owe the theory of positive and negative electricity,
and the fact that they are always generated in equal amounts, a law
whose importance can scarcely be estimated. He investigated the Ley-
den jar, and showed that the coatings had equal positive and negative
charges, and explained the fact that the jar cannot ho charged when
the outside coating is insulated. Ho invented the charge and discharge
hy cascade and showed that it was the glass of the jar and not the
coatings which contained the charge. He discovered tho property of
points in discharging an electrified body, and the identity of lightning
with electricity. He also made the first experiments upon atmospheric
electricity.

To Canton is due the honor of giving the first experiments on induc-
tion, but Franklin is tho first who gave the general law of this species
of action. Truly our country and this city should honor the memory
of this man.

But it is not my purpose to repeat to you in detail the familiar history

Henet a. Eowland

of our scieace. Thus far no important applications of electricity had
been diseoTered; there was nothing but pure science to attract inTes-
tigators, and thus the science remained for many years after.

But no science is complete unless it is quantitatiye as well as quali-
tative. It is now very nearly one hundred years since Coulomb laid
the foundation of electrostatics and Aepinus and Cavendish commenced
to lay the foundation of mathematical electricity, and they were fol-
lowed by Laplace, Biot, Poisson, and Murphy.

The discoveries by Oalvani and Volta in 1790 and 1800, and by
Oersted in 18^0, gave us the galvanic battery and electro-magnetism,
and it was not until the latter date that any useful practical application
was possible. Then, so complete was the science that no factor of other
than minor importance was necessary to transmit intelligence from one
extremity of the earth to the other.

By the labors of the immortal Faraday, electro-magnetic induction
was discovered and the modem dynamo-electric machine became a cer-
tainty.

To his other labors, both experimental and theoretical, the modem
science of electricity owes much, but it is familiar to all. The name of
Faraday needs no eulogy from me, for it stands where it can never he
hidden, and the spark which Faraday first kindled now dazzles us at
every street corner. No wealth came to him, though he had only to
hold out his hand for it. But the holding out of one’s hand takes time,
which Faraday could not spare from his labors, and so the wealth which
was rightly his went to others. Who will follow in his footsteps and
live such a life that the thonght of it almost fills one with reverence?
It is not only his intellect which we admire; it is his moral qualities
which fill us with awe — ^his noble and unselfish spirit.

The name of Faraday brings us down to modem times, whose history
it is unnecessary to repeat in detail, especially as there are some now
present who have contributed largely to bring tho science to its presemt
perfection.

One of the principal features which we remark in our modern science
of electricity is the perfection of our means of measuring both electrical
and magnetic quantities. In this connection the groat names of Gauss
and Weber appear, the fathers of the modern absolute system of eloc-
trical and magnetic measurement, and that of Sir William Thomson,
in no less degree distinguished. On the laws of electric attraction we
base our electrostatic system of measurement, and on tlic magnetic ac-
tion of the current, the great discovery of Oersted, we base our electro-

EI/BOTEIOAL CJON-PEBEN-Ol AT PHILADELPHIA 627

magnetic system, and we connect these two systems by that great physi-
cal constant, the ratio of electro-magnetic to the electrostatic system of
nnits.

What can be simpler in theory than the electrostatic system, based,
as it is, on the law that electric attraction varies inversely as the square
of the distance? We only have to know how the electricity is dis-
tributed and Its attraction is known. Hence we must select the simplest
possible case, such as two parallel disks, and to render the problem cal-
culable, we add a guard ring to the movable disk. We then have the
absolute electrometer of rhomson. This gives us a measure of the
electric potential. Knowing the capacity and difference of potential
of the surface of a condenser, we know its charge. But all these quan-
tities, the calculation of the electrometer and the capacity of the con-
denser, depend upon the mathematical theory of electric distribution.
Are we able to calculate the capacity of condensers of all forms? I am
sorry to say we are not. The modem method of treatment is due to
George Green, an English investigator, whose name should be held in
honor by all electricians. But this method is what is called an inverse
one. It is not a method by which we can calculate the distribution
on any body at random, but the shape of the body and the electrical
distribution on it arc both found at once by a species, as it were, of
exploration and discovery. So that we cannot make our oloctrometeis
and condensers of any shape and then calculate them, but wo are forced
to make them of some simple geometrical form whose solution is
known. We fit our apparatus to the mathematics rather than the mathe-
matics to the apparatus.

But when we have satisfied all the conditions wo Tnoasuro out our
static charges as easily as a quantity of matter. The niainrfacturor sells
the oxygen and hydrogen in iron cylinders and doterminos the amount
by the product of the capacity of the cylinders by the prossuro. Were
there any buyers of electricity wc might sell them a Ijoydcn jar full and
determine the amount by the product of the capacity of the jar by tho
electric potential. According to this analogy, then, tho electricity is
similar to matter and the potential fluid pressure, while the word ca-
pacity has a similar meaning in both.

In the electro-magnetic method of eloctricnl moasurement we make
use of the magnetic action of the current, cither on a neighboring mag-
net or another current or portion of tho same current. The laws of the
action of a current on a magnet wore (liscovei-od hy Biot and Savart,
and of two currents on each other by Ampcjrc, and the results applied to

Hbney a. Eowi/AN'd

piactical naeasurement to-day gi^e as galvanometers of all kinds and
tLe electro-dynamometer of Weter. By the galvanoiaetor we can meas-
ure the q^uantity of electricity passing at any moment, hut by the elec-
tro-dynamometer we measure the integral square of the current, a
quantity on which the heating of the circuit and the energy expended
depend.

Thus the electro-dynamometer measures the energy from an alternat-
ing current dynamo-electric machine as easily as from one giving a con-
timiouB current, hut to know this energy we must know something else
besides the integral square of the current, and this is c^ithor tlic rt^Kisi-
ance of the circuit ox the electromotive force. But the ineasureinent of
electromotive force depends on a resistance. The question then comos
up as to what unit of resistance is the proper one. Hero we have to
refer to the mathematical theory of the subject, and the great law of the
conservation of energy tells us that what is known as the absolute unit
of electrical resistance is the proper one for use in this case. Hence
the great practical use of deterndning this unit. The experiments of
Kirchhoff, Weber, Kohlrausch, and the Britiph Asflociaiion found a
value from 1 to 3 per cent too large.

Many years ago I myself experimented on the subject, and obtained
a result about 4 per cent too high. Recently Tjord Rayleigh has taken
up the matter and made a series of experiments of unparalleled accu-
racy in this line. The International Commission, dotorminod on by the
Electrical Congress in Paris in 1881, met in April of this year at Paris,
and has now given us a legal ohm defined as being the resistance of a
column of mercuiy 106 centimetres long and 1 milliinolre in seetion nt
0® 0- The length best satisfying the experiments is aboxit 100*25, but
it was considered best to use the round number. The oxporimoids
which I bave been making under an appropriation from the (lovc'.rnnuuit
are now barely completed, but they will probably a.gr(*<j very W(dl with
the latter figure. Hence, we can say that we now know ibis unit of
resistance to one part in one thousand, at least. And so wo are in a posi-
tion to measure the energy of a current to the same degree of accuirncy,
as far as this quantity is concerned.

But to measure a current by the tangent galvanomot.or one rcMjiiiros
to know the intensity of the earth^s magnetism, a quantity difiicull to
determine and constantly varying with time and place. The (declro-
dynamometer, when made with care, is excellent, but a good one is im-
mensely expensive. Our methods, then, of current moasuroment arti
bad, unless carried out in a completely equipped pliysieal lal^onitory.

Eleotrioal Conpbrbnob at Philadelphia

6»9

Vith a practical standard of electromotive force, such, as a Clarkes
standard cell or a thermo-electric battery, this difBLcnlty partially van-
ishes. Better, perhaps, we might make simple electro-dynamometers
with constants determined by comparisons with a more costly instru-
ment.

But where shall these standards be kept? Evidently the Q-ovem-
menl^ which decides on our standards of weights and measures, should
take in charge the electrical standards, and possibly also the thermo-
metric standards. The formation of such a Bureau of Physical Stand-
ards will be brought to the attention of this Conference.

Having given certain standards then, the measurement of currents
and current energy becomes easy. The amount of heat generated in a
wire of known resistance hy a known current is also easily found from
the absolute system of electrical measurement.

Besides the two so-called absolute systems of measurement of elec-
tricity and electric currents, we have also one based on the chemical
action of the current whose laws were discovered by Faraday. Know-
ing the electro-chemical equivalent of some substance, we are able to
measure the time integral of the current or the total quantity of tho
current which has passed.

The absolute measurement of magnetism is equally simple with that
of electricity, and it is a common observation to find the eariih^B magnetic
force. But Faraday has put in our hands a very simple method of meas-
uring a magnetic field, and to-day all are familiar with In’s beautiful
laws with respect to magnetic lines of force. Wo know tho laws of
electro-magnetism, and just how many lines of force (better induction)
can pass through a piece of iron of given cross-section, and what is their
relative rosipbnioo wlion, passing through a.ir or iron. Tn fact, we have
all that is necessary for a complete theory of the clynamo-clectric ma-
chine, and consequently wo find that tho latter agrees perfectly with
theory, and no fact has boon observed with reforouct^ to it which could
not have been foreseen from theory by a person of proper intelligence.

This part of electrical science, the measurement of olcctrical and mag-
netic quantities, is thus in a very forward state, based, as it is, on the
mathematical theory of the subject. But, in reality, this forms but a
very small portion of our science. Shall we bo contented with a simple
measurement of that of wliich wo know nothing? T think nobody would
care to stop at this point, although he might bo forced to do so. The
mind of man is of a nobler cast, and socks knowledge for itself alone.
We are not so l)ase as to be honest because Honesty is tho best policy,”

630

Hbney a. Eowlani)

neither are we so ignoble as to seek knowledge “ Knowledge* ‘w

— two sayings which aro certainly true, but low luul sordid in

their tone.

We have, then, the beautiful fabric of inatlicniatical electricity given
to the world by Poisson, Oreon, Ilolmholtis, ThoniHon, Maxwell, and
others whose names are immortal. No liypoihcsiH as to the natnn* ot
electricity rests at its base. Starting from the most siinplt* laws of
electricity and magnetism, it rises from a stablu fouiulation and nmrs
its form high in the air, never to bo overturned, whale v(*r the fall* of
the so-called electric fluid or the ultimate theory <»r magnetisnu On the
simple fact that there is no electric force inside a (dosed conductor, it is
proved that the electric attraction and repulsion varies invcrs(dy as the
square of the distance. The fact, is sufliciont to givc^ us thc^ wliolt^ tht*ory
of electrostatic distribution on conductors.

From the simple fact that we can break a magiu^t up into parts whicdi
are similar to each other, and that these parts attract and reptd mvh
other in a certain manner, we derive many important facts with rcgiinl
to magnetism.

From the magnotic action of the current wo find* by an a))pricuiion of
the great law of conservation of energy, all the laws of imlnccd t*ur-
rents, either from magnets or otlun* (uirrcnts. By an iilmosi supt‘rhu-
man effort of tho intellect wo detatth our (detdrie currents from nialti*r,
and supposo them to take place in tho clhor of spams and w«* have the
grand electro-magnetic tlioory of light given to us hy MjikwcII.

But the subject is too vast to be IroaWd in a moment. Stiflice ii
say that no person at tho present day has tho right t«» oxpn*ss an opin-
ion on any theoretical (piostiou connottiotl with tdoeiru^ily wiiht»ut a
knowledge of its inathonmties.

This study has loci us to alter our ideas on many (iu«»slions. Wlmi
is the mochanisni of idocdric or inagmdio atlrntdi^m? Faraday haw
given us his idea of linos of forces, and 1ms nuuh* IIhmu play an iuipitrfant
part in the theory of niagmdic induction. When treated nmtiieiiiati^
cally, Maxwell has shown that all (di^cdrio and magnetie ntlraeti*>nH can
Im explained by a tension along tho lin<»s of force and preMwun* at right
angles to them — an idea duo to Faraday.

The mathematical theory of these liiuw shows I hat all eleetmstatii’
forces between either condxictors or non-conductors can he e\(dninf‘d in
tins mannor. As the laws of magnetic attraction an^ the same in every
way as electrostatic attraction, if W(5 should do away with elect rii*
duetion, it follows that magnetic attraction is to bt» ex|daiiM*d in exactly

EleoteicIl Conpbebnob at Philadelphia

631

the same manner. In obtaining this result Maxwell calcvilated the
forces acting on the medium at every point, and compares these with
imaginary stresses in a medium at the given point. Hence, the energy
stored up can he represented either as due to the mutual attraction of
the electricity at a distance, or to the stresses in the medium at every
point, and thus, as Thomson has shown, by a volume integral of the
square of the force at every point. Hence, we are at liberty to deny
the existence of all action at a distance, and attribute it to the inter-
vening medium, which, to be logical, we must assume to be continuous
and not molecular in constitution.

Thomson has pointed out that magnetism must be of the nature of ro-
tation, such as possibly vortex motion in a fluid, and Maxwell has done
something toward making a mechanical model of such a medium. Thom-
son’s wonderful address at Montreal has also given us much to think of
in the same direction.

But hero wo have reached the limit of our science, and even that serv-
ant of our reason, imagination, fails us. We are yet unable to picture
to ourselves what takes place in a medium subject to electrostatic ac-
tion. Wo are face to face with the great problem of nature, and the
questions, What is matter? What is electricity? evoke no answer from
the wisest among us. Our mathematics has guided us safely up to a
certain i)oint and will guide us still further; science will advance and
we shall know more. But, for the i)rosent, this is the limit which wo
have yet attained in this direction. However, the idea of a medium is
still serviceable in other portions of our science.

We have seen that the medium explains the electriciil and magnetic
attraction of bodies at rest. The question then comes up as to what
happens in the medium when those bodies move. Arc the imaginary
stresses in the medium transmitted from place to place instantaneously
or do they require time? Mathematics in the lunicls of the immortal
Maxwell has answered this question, and we now know that any mag-
netic or electric distruhance is propagated through space with a velocity
equal to the ratio of the eloctro-magnetic to the electrostatic unit of
electricity. This groat physical constant haw now been found by experi-
ment to he equal to the velocity of light, and thus has arisen that great
modem theory. Maxwell’s electro-magnetic theory of light. Jndeod, at
the present day, so perfectly does this theory agree with experiment that
we can almost regard it as a certainty. The velocity of light and the
ratio of the units agi*ee far within the limits of experimental error. The
fact that bodies having a true (not electrolytic) electric conduction are

632

Heney a. Eowlayd

always more or less opaque, the refraction and dispersion of light, dou-
ble refraction, and diflEraction, all are explained on this theory with an
ease and simplicity wanting in all other theories; and, lastly, an elec-
tro-magnetic phenomenon has been discovered, which, when applied to
this theory of light, explains the rotation of the plane of polarization
produced by a magnet. There is no fact in nature seriously in disagree-
ment with this theory, and it serves to connect two of our most impor-
tant branches of physics, light and electricity.

But some physicists say that it is not a true theory, because it is not
mechanical, the object of these physicists being to reduce every phe^
nomenon of nature to matter and motion. Whether this is necessary or
not I leave to the philosophers. But it is to be noted that the old me-
chanical theory that light is a vibration in a medium having the prop-
erties of an elastic solid is not entirely at variance with the new theory.
The medium we call ether. The electro-magnetic theory says that
the waves of light are waves of electric displacement, while the old
theory says they are waves of ether. Make electricity and the ether
equal to each other and the two theories become one. We have arrived
at that hazy and xmsatisfactory theory of Edlund that ether and elec-
tricity are one, except that by this theory electricity is presented to us
as an elastic solidi

But the ground trembles beneath us, and we shall soon be plunged in
the mire of vague speculation if we do not draw back.

Among the other questions which depend for their solution on the
presence of a medium may be mentioned the mutual action of two elec-
trified bodies moving in space. It has been found that electricity car-
ried through space on a charged body has exactly the same magnetic
effect on a stationary magnetic needle as if it had been conducted.

But when electrified bodies move uniformly forward in space, we can
conceive of no mutual eifect from such motion unless it is relative to a
medium, for we cannot even conceive of absolute motion.

AssumitTg the medium to exist, we then know that a positively aud a
negatively charged body flying through space with the velocity of light
would have their electric attraction just balanced by their magnetic re-
pulsion, and so would exert no force on each other.

But it is a most wonderful fact that we have never been able to dis-
cover anything on the earth by which our motion through a medium
can be directly proved. Carried, as we suppose, by the earth with im-
mense velocity through regions of space filled with ether, we have never
yet been able to prove any direct influence from this ethereal wind.

Electrical Conferenob at Philadelphia

633

The assumption of a medium allows us to solve in some cases that
pro)>lem so long under discussion hy electricians — ^namely, the true ve-
locity of an electric current. We now know that tlie term velocity
hardly applies to this case, and that the current arrives at different
points so gradually that wc know not when to say it has arrived. But
there is certainly a minimum time when even an infinitesimal current
can reach a distant point. Suppose two wires stretched in space with
their ends near together at one end and a Leyden jar be discharged from
one to the other at the near end. The minimum possible time of obtain-
ing a spark at the distant end will evidently be the time required by
light to pass from the Leyden jar to the distant point, not around the
wire, but in a straight line. In this ease the greatest maximum velocity
is thus twice that of light reckoned around the wire, and may be any
amount greater when we bend the wire. For all ordinary distances this
velocity may be considered infinite, and the retardation to depend
only on the electrostatic capacity and magnetic self-ihdnction of the
wire. Treated in this way, we have Thomson's mathematical theory
of the propagation of an electric wave along a telegraph wire or cable,
a theory of great practical use in telegraphy and telephony. But until
the action in the external medium is also taken into account, it can only
be considered an approximation. For we can never move a magnet,
discharge a Ixiydcn jar, or complete the circuit of a battery, without
causing a wave of electro-magnetic disturbance in the ether, and every
signal which is sent along a telegraph line is acjcornpanied by a wave in
the ether, which travels outward into space with the velocity of light.
Truly the idea of a modiuin is to-day the keystone of electrical theory,
but wo can hardly suppose tliat it has even yet attained a fi’action of
the importance to which it is destined to rise.

Tjet mo now call your attention to one of the most wonderful facts
oonnoctod with electrical science. When wo arc dealing with the elec-
trostatic action of electricity, we find that it is the so-called electric fluid
which attracts the opposite. Not only do wo observe the attraction of
bodies oi)positely charged, but the electricity itself on the two bodies is
displaced by its mutual action. But when we come to investigate the
mutual attraction or repulsion of oloctric cun^ents on each other, we find
an entindy difforont law. Tn this ctisc the conductors carrying the cur-
rents attract or repel each other, but the currents within those con-
ductors have no influence of attraction or repulsion to displace them-
selvos within the body of the conductor. In other words, the current
is not displaced by the action of a neighboring magnet, but flows on
calmly as if it were not present.

634

Hbnby a. Eowland

This to me is one of the most wonderful facts in electrical science, and
lies at the foundation of our science. It cannot he ignored in any fur-
ther progress we may make in electrical theory, but points out a radical
difference between electrostatic and electro-magnetic action.

I have said there is no action of a magnet in displacing an electric
current, and have thus stated the broad general fact, and which is per-
fectly true in some metals. But in others tliere is a small action which
changes in direction with the material. The elements of the electric
current within the material are rotated around the lines of magnetic
force, sometimes in one direction and sometimes in the other, according
to the material. But the action is, in all cases, very weak. When ap-
plied to the electro-magnetic theory of light, this action leads to the
magnetic rotation of the plane of polarization of light. As to the ex-
planation of both these actions, Thomson has remarked in the case of
light, from dynamical considerations, the rotation can only come from a
true rotation of something in the magnetic field, and leads us to think of
all magnetic action as of the nature of vortex motion in a fluid. But
here our theory ends for the present. We have obtained a clow, but it
is not yet worked up.

I have now taken a rapid glance at some of the modem advances of
electrical science, and we liave not yet had to give up the old idea that
electricity is liquid. To the profound thinker this idea is very vague,
and there are some facts at variance with it, but it is still UHofiil. Wo
often hear persons say that this old idea is gone, and that electricity is

force,'" whatever they may mean by that. But let us see. The work
or energy of an electric current between any two points is the quantity
of electricity passed multiplied by the potential; this work goes to
heating the wire. Let a cunent of water be passing in a pipe, and the
quantity of water multiplied by the difference of pressure between two
points ^ves us the work which has been done in the intervening space,
and which has produced heat. The analogy is complete. KTo electricity
has been destroyed in the one case, or water in the other, but the work
has come from the fall of potential in the one case, and the fall of
pressure in the other; the resultant is the same in both— heat. Again,
we can obtain work from the mutual attraction and repulsion of elec-
trified bodies, and the work in this case always comes from the change
0 potential between the bodies while the electric charges remain undis-
turbed m quantity. Electricity, then, is not energy, but is more of the
nature of matter.

So far for electricity in the state of rest or steady flow. But when it

ElbotricxVl Conference at Philadelphia

635

changes from rest to motion, all kno*wii liquids have a property kno-wn
as inertia; fin*thermore, they have weight. But the electric fluid has
neither inertia nor weight as far as we have yet experimented, and in
this respoct differs from all known matter. Purthermore, we have never
yet been able to separate electricity from ordinary matter. ‘When we
pass electricity through a vacuum, the resistance becomes less and less,
and one may have hopes of finally having an electric current through a
vacuum. But, as the exhaustion proceeds, we observe that the resist-
ance begins to increase until it reaches such a point that no discharge
can take place. Electricity cannot exist, then, without matter, a fact
fatal to the idea o-f a fluid, however useful that may be. Wc have but
one conclusion from this, and that is that eheiridiy is cu property of
matter. Do with it what we may, it can never be separated from matter,
and when we have an electrical separation tlio lines of force must always
begin and end in matter.

Tlie theory of matter, then, includes electricity and magnetism, and
lioncc light; it includes gravitation, heat, and chemical action; it forms
the great ])roblem of the universe. When we know what matter is,
then the theories of light and heat will also be perfect; thou and only
thou, shall we know what is electricity and what is magnetism.

It is the problem of the universe which looms up before us and before
which we stand in awe. The intellect of the greatest among us ap])cars
but feeble and we all, like Newton, appear but as children on the sea-
shore. But how few of us find the shells which Newton did, and liow
few of us try. The problem is vast and the moans for its solutioTi must
1)0 of corresponding magnitude. Our progress so far has been but small.
Wlien WG push our inquiry in any direction wo soon roach a limit; the
region of the unknown is infinitely greater than the known, and there
IR no fear of there not being work for the wliolc world for centuries to
come. As to the j^ractical applications which await ns, the telegraph,
tlic telephone, and electric lighting, are but ehihrs play to what the
world will see in tlie future.

But what is necessary to attain those results? We have soon how the
f oeble spirit, which was waked up by frietion in the amber and wont forth
to draw in light bodies, has grown until it now dazzles the world by its
brilliancy, and carries our thoughts from one extremity of the world to
the otlicr. It is the gonhis of Aladdin's Itnnp which, whim thoroughly
roused, goes forth into the world to do us service, and returns bearing
us wcaliii and honor and riches. But it can never be the R'rvant of an
ignorant or lazy world. Like the genius of Aladdin ^s lamp it appeared

636

Hbnbt a. Eowland

to the world when the amber was rubbed, but the world knew not the
lan^age in which to give it orders, and was too lazy to learn it. The
spirit of the amber appeared before them to receive its orders, but was
only gazed at in silly wonder, and retired in disgust. They had but to
order it and it would have gone to the uttermost parts of the earth with
almost the velociiy of light to do their bidding. But in their ignorance
ttey knew not its language. For two thousand years they did not study
it, and when they then began to do so it took them two hundred and fifty
years to learn the language sufRciently to make a messenger of it. And
even now we are but children studying its ABC. It is knowledge,
more knowledge, that we want.

I have briefly recounted the advances which wer have now made in
one science, and, however beautiful it may appear, we have soon reached
the limit of the known, and have stood in wonder before the vast un-
known. For very much of our science we see no practical applications,
but we value it no less on that account. We study it because we have
been gifted with min ds whose exercise delights us, and because it seems
to us one of the highest and noblest of employments. And we know by
the history of the past that the progress of the world depends on our
pursuit, and that practical applications, such as the world has never even
conceived of, await us. It is necessary that some should go before to
clear the way for the world’s advance.

This is the work of the pure scientist; to him the problem of the uni-
verse is worth devoting hie life, and he looks upon wealth as only add-
ing to his means of research. He hopes not to solve the problem him-
self, but is contented if he may add some small portion to human knowl-
edge; if he may but do hie part in the march of human progress. He
looks not for practical applications, but he knows full well that his most
abstruse discoveries will finally be made useful to mankind at large, and
so troubles himself no further about it.

The science which he creates is studied by others. Their minds are
educated by it and their hearts entranced by its beauties. And Some
are led to devote their lives to its.further advancement. But the whole
world benefits by it intellectuaUy. The wayward spirit of the amber
has vanished forever, and prosaic, law-abiding electricity has taken its
place even in the estimation of the most ignorant. The world has ad-
vanced, and in great part from the study of science.

Then comes the practical man, who sees that other benefits can be
reaped besides those of pure intellectual enjoyment. While the inves-
tigator toils to understand the problem of the universe, the practical

Electrical Conference at Philadelphia

637

man seeks to make a servant of onr knowledge. He seeks to increase
the power of our bodies and to make the bonds by which the mind is
•united to it less irksome. It is he that increases the wealth of the world,
and thus allows those so disposed to cultivate their tastes and to elevate
themselves above the savages. The progress of the world depends upon
his inventions.

Let not, then, the devotee of pure science despise practical science,
nor the inventor look upon the scientific discoverer as a mere •visionary
person. They are both necessaiy to the world^s progress and they are
necessary to each other.

To-day our country, by its liberal patent laws, encourages applied
science. We point to our inventions with pride, and our machinery in
many of the arts is not surpassed. But in the cultivation of the pure
sciences we are but children in the eyes of the world. Our country has
now attained wealth, and this wealth should partly go in this direction.
We have attained an honorable position in applied science, and now let
us give back to the world what we have received in the shape of pure
science. Thus shall we no longer be dependent, but shall earn our own
science as well as inventions.

Let physical laboratories arise; let men of genius be placed at their
head, and, best of all, let them be encouraged to pursue their work by
the sympathy of those around them. Let the professors be given a
liberal salary, so that men of talent may be contented. Let technical
schools also be founded, and let them train men to carry forward the
great work of applied science.

Let them not be machines to grind out graduates by the thousand,
irrespective of quality. But let each one bo trained in theoretical
science, leaving most of his practical science to be learned afterward,
avoiding, however, overtraining. Life is too short for one man to know
everything, but it is not too short to know more than is taught in most
of our technical schools. It is not telegraph operators, but electrical
engineers that the future demands.

Such a day has almost come to our country and we welcome its ap-
proach.

Then, and not till then, should our country be proud and point with
satisfaction to her discoveries in science, pure and applied, while sht^
has knowledge enough to stand in humiliation before that great iindis-
covered ocean of truth on whose shores Newton thought he had but
played.

THE ELECTRICAL AND MAGNETIC DISCOVERIES OF

FARADAY

ADDRBBS AT THE OPBNIEG- OP THE BLBCTBIOAL CLUB HOUSE OP
NBV TOBK CITY, 1888

lEUctrical JSeview, New- Tork, Feb. 4, 1888]

In tlie progress of all sciences tliere axe epochs when men, thoroughly
fitted by nature, if not by education also, for the most successful study
and advancement of their science, are bom into the world, and by their
natural talent, perseverance and love of their science, give it an impetus
which stamps their name forever on its history. But, however great
they may be, we know enough of the nature of scientific progress to he
sure that there never was one of such greatness as to be absolutely neces-
sary to human progress. The world would never have stood still on
account of the absence of any name from its annals, and even the place
of the immortal ITewton would sooner or later have been filled by others,
and all the discoveries of his Prineipia have been known to us now,
even had he never existed.

Discoveries, then, have their origin not only in the presence of men
of exceptional genius in the world, hut in a true and overwhelming
progress of science which marches forward to the understanding of the
universe, irrespective of the efforts of any single individual to promote
or retard it. It is a great fact, whose explanation we find in the craving
of mankind for knowledge of nature and power over her.

As men of genius are born, they find the discoveries of those who
have gone before them awaiting them. They join in the good work,
and add their efforts toward the advancement of knowledge. But in all
cases they start at the point where those who have gone before them
have left off; if their work is good they continue it; if it is bad they
replace it by better, that the structure of science may be reared on solid
foundations, and grow surely and steadily toward a perfect whole.

To understand, then, the place of any man like Faraday in the history
of science, we must also understand, the state of that science at the time
when he did his work.

Michael Faraday, the son of a smith, was born in 1791, and was ap-
prenticed to a bookseller and bookbinder in 1804. He educated himself
by reading, and became the assistant of the great chemist. Sir Humphry

Eleotbical and Magnetio Disooyebies op Eabadat 63^

Davy, when he was twonty-two years old. His attention was first given
to chemistry, hut was finally attracted to electricity by the discovery of
electro-magnetism by Oersted, in 1820. At this period the subject of
electrostatics was very far advanced even as compared with modem
times.

More than 200 years before, Gilbert had commenced the study of
electricity, and divided bodies into electrics and non-electrics, accord-
ing as they prodnced or did not produce electricity hy friction. Uearly
100 years before, Stephen Gray had discovered the difference between
conductors and non-conductors, and had shown the means of carrying
electrical effects to a distance of several hundred feet hy means of a con-
ducting thread or wire suspended hy non-conducting threads of silk.
Otto von Guericke, du Pay and Wilke had shown that there were two
kinds of electricity — ^resinous and vitreous. The Leyden jar had been
discovered by the Dutch philosophers. Franklin had writteil his cele-
brated series of letters on electricity, explaining the phenomenon of the
Leyden jar and induction as clearly as we can do it at present, giving
his theory of positive and negative electricity to the world, and demon-
strating in the most perfect manner the electrical nature of thunder
and lightning.

Aepinus and Cavendish had applied mathematics to the subject, and
the latter had discovered the law of inverse squares, and made for himself
a series of graduated coudensers, by which lie measured the capacity of
differently shaped bodies. They had l)cen followed by Laplace, Pois-
son and Biot in mathematical olectricity. Coulomb had introduced his
torsion balance, the first accurate instrument for electrical measure-
ment.

Galvani and Volta had sliown how to produce a current of electricity
by the galvanic battery. The chemical action of electricity had long
been known, and had been forcibly brought before the world by the
immortal experiments of Davy only a short time before, and Bitter had
discovered polarization and ihe storage battery.

But, although many persons had suspected that there was some con-
nection between electricity and magnetism it was not until Oersted, in
1820, discovered tlio nature of this eonnection, and AmpSre had given
the laws of the attraction of currents, that the seionce of electro-mag-
netism bocamo a subject o£ investigation. This new discovery aroused
the attention of the scientific world to another field of research, and
especially awakened in Faraday that sublime curiosity with respect to its
laws, which finally led him to his first discovery in this subject.

640

Hbitey a. Eowlaitd

The new fact of electro-inagiietism interested him. Soon he found
that the turning of the needle, as found by Oersted, could be accounted
for by the attempt of the north pole to revolve around the vire in one
direction and the south pole in the other. Not content with demon-
strating the theory, he invented some pieces of apparatus by which
this revolution could be realized, and every collection of physical appar-
atus now has them. The little wires or magnets hanging in the cups of
mercury are familiar to all^ and form the first notable instance of a
continuous rotary motion produced by the electric current; it was the
first form of electro-magnetic motor so common in our day. But wo
can not call this a great discovery, as the piinciples were very apparent.

Eight or nine years now passed before Taraday gave anything of
importance to the world in the subject of electricity and magnetism.

Seebeck discovered thermo-electricity. Ohm discovered the law con-
necting electro-motive force, resistance and current, and the whole
scientific world was alert to discover new facts. Faraday brooded on
the subject: the electric ciii'rent produced magnetism, why should not
magnetism produce an electric current? At the present age of the
world we could answer this question at once, by aid of the great law of
the conservation of energy. But fifty-seven years ago it was unknown,
except in a very vague manner; the foreshadowing of this great law
soon came into the mind of Faraday, but at this period he could only
grope blindly in the dark. He knew that a piece of soft iron became
magnetic in the presence of a magnet, and that a conductor was electri-
fied by induction when near a charged body. Eeasoning by analogy,
why should not a conducting circuit have a current generated in it in
the presence of a wire carrying a current? This was Paraday^s reason-
ing, and he proceeded to test it by experiment. Winding two wires
side hy side, on a cylinder of wood, he passed strong currents of elec-
tricity through one of them, and attached the other at its two ends
to a galvanometer. The slightest permanent deflection was observed,
and many a man would have pronounced the experiment a failure.
But Faraday was not of that nature; he tried again and again, and
while bending over the galvanometer in a vain effort to see a slight
permanent deflection, he noticed a little jerk of the needle, almost too
small to be noticed. His attention was arrested by this curious action,
and he proceeded to investigate it.

He found that this slight movement of the needle was in one direc-
tion on making the current, and the opposite direction on breaking it.
He substituted a helix, enclosing an unmagnetized needle for tlxe gal-

Eiboteioal and MAaNBTic Disoovbbies of Faraday 64:1

vaaometer, and he found that it was magnetized by this electrical wave,
at the moment of making or breaking the main cirenit.

But Faraday was not content until he had discovered all the laws
of this new action; he placed two wires on boards, so that, when near
together, they were parallel to each other. He now found that the
action took place, not only when the current was interrupted, hut also
when one wire was moved with respect to the other.

So far, the new effect had only been obtained near an electric current.
But Faraday did not forget the connection between electricity and
magnetism, but now proceeded to give a new aspect to his discovery.

For this purpose he chose a ring of wrought iron ou which he wound
two coils of wire which he attached to a battery, and to a galvanometer,
as before. From the presence of the iron, however, he obtained an
immensely greater ejffect than at first, so that, instead 0 ‘f an almost
microscopical deflection, the needle of the galvanometer whirled around
three or four times, and ou attaching two points of charcoal to the ends
of the secondary wire, he ohseived a minute spark between them on
completing the main current. The same increased effects occurred on
placing bars of iron in straight co-ils of wire, and Faraday had now
proved that the new effect was dependent on the magnetic action of
the current

He now made one step further, and showed that these induced cur-
rents could be obtained from permanent magnets without the aid of
other current^ by the simple motion of a wire near a magnet, and that
they were specially intense when the wire was wound on a soft iro-n
cylinder, which was then moved near the poles of a magnet. Not con-
tent with observing these currents by a galvanometer, he obtained a
powerful permanent magnet and allowed his bar of iron, wound with the
coil, to come in contact witb the poles, the circuit being broken at the
same instant. A spark was observed at this broken junction every time
the bar came down on the poles. Tyiulall tells a very curious story of
this experiment which we can well recall. Faraday was attending a
meeting of the British Association in Oxford, in 1838, and was re-
quested to show some of his wonderful results to the scientists there
gathered. "While he was thus occupied a dignitary of the University
entered and inquired what was going on. Prof. Daniell, who was
standing near, explained the matter in popular language. The Dean
listened with attention, and looked earnestly at the brilliant spark, but
a moment afterwards he assumed a serious countenance, and shook his
head: I am sorry for it," said he, as ho- walked away; I am sorry for
41

642

Henry A. Eowland

it; indeed I am sorry for it; it is putting' iiew arms into the hands of the
incendiary/^ This occurred a short time after the papers had been
filled with the doings of the hayrick burners.

Now, after more than fifty years, the spark of Faraday blazes at every
street comer, but it has never been found more efficient than an ordinary
lucifer match in the burning of hayricks.

. Paraday's attention was now called to the explanation of a curious
action discovered by Arago, who found that a rotating disk of copper
carried a magnetic needle with it when the latter was suspended over
it. The explanation had never been obtained, but Faraday now saw
that it was but an instance of his newly discovered action. In order
to show that currents were induced in the revolving plate, he mounted
it between the poles of a magnet and connected the centre with one
pole of a galvanometer; on pressing a wire from the other pole to the
edge, Faraday obtained a continuous current of electricity. This was
the first continuous current dynamo ever constructed.

But he rested not until he had obtained the laws of induced currents
and expressed them in such simple language that they have ever since
been the admiration of the scientific world.

In giving the law of the production of these induced currents, Fara-
day for the first time made use of his famous lines of force, although
he here calls them magnetic curves.

He showed that a wire must cut these lines in order to have a current
induced in it. In order to account for the induction in neighboring
wires on making and breaking an electric current, he pictured in his
mind the lines of force mo-ving. The current could only start gradually
after contact was made, and while it was increasing the lines of force
always closed on thLemselves in rings, were expanding outwards cutting
any wires near it, and inducing currents in them. When the current
was broken, the lines contracted and produced contrary induced cur-
rents.

In after years he made his law quantitative, and proved that the
integral induced current was in proportion to the number of lines of
force cut by the wire.

In his papers of 1831-2 I find these lines always called magnetic
curves, and his laws of induced currents are given in terms of these
curves. This idea of lines of force was . ever after one of the priucipal
points around which the mind of Faraday revolved. He applied it to
electrical action as well as to magnetic, and wc see him in aftei' years
striving to do away with action at a distance, and substitute for it a
medium filled with these lines of force.

Elbotbioal and Magnetio Disogvbeibs op Faraday (543

The medium subjected to electrical or magnetic forces is, according
to Faraday’s idea, polarized in the direction of these lines of force, so
tliat each particle only has to act upon the one ne 3 ± to- it in order that
the force may be transmitted to any distance. In Faraday’s mind these
lines had not only an imaginary existence as being the direction in
wliich the north pole of a needle or an electrified particle tended to
move in space, but also a real existence. He imagined them as elastic
bands repelling each other laterally, and binding the north and south
poles of a magnet, or the positive and negative electricities, together.

It 'was only in after years that he discovered all the properties of these
lines, and I shall therefore return to them again.

Guided by these lines of force, he investigated the subject of in-
duced electric currents in so complete a manner that nothing of funda-
mental importance has ever been added to the subject. True, to-day
we understand the subject mtich better than Faraday ever did. The
mathematical researches ot Helmholtz, Tliomson, Maxwell and others
have thrown a flood of light upon the induction of electric currents,
and the law of the conservation of energy gives us means of proving all
its laws, and indeed of showing that magneto-electric induction is the
conse(jU6nce of the magnetic action of the current as discovered by
Oersted.

But fifty years ago this law of the conservation of energy was too
little known to be used in this way. It required the support of just
such experiments as those of Faraday to bring into existence and to
prove it. Hence, Faraday had but littie to guide him to the discovery,
except that subtle reasoning of a man of genius which ahnost amounts
to instinct.

The difference of common and voltaic electricity next engaged his
attention. A Leyden jar highly charged might have large sparks and a
loud sound; it might ignite alcohol and -produce a strong shock when
passed through the human body, but it was almost incapable of decom-
posing water, and could scarcely affect a magnetic needle. The voltaic
battery, on the other hand, could produce the latter effects, but not the
former.

How did these two kinds of electricity differ?

Faraday answered this by producing all the effects with one kind of
oleetrieity that could be obtained from the other. He showed that the
difference was caused by there being great tension, or, as we call it,
potential in one case, with very little quantity, while in the other there
was great quantity with low tensio-n. By charging Leyden jar batteries

644

Hbnet a. Borland

of different sizes mth the same number of turns of his machine, and
dii^nTiarging them through a galvanometer, he proved that the sudden
deflection O'f the instrument depended on the quantity, and not the
tension, of the electricity. He then arranged a little voltaic battery out
of zinc and platinum -wires, so that, when joined to the galvanometer for
three seconds, it gave the same swing to the needle as the Leyden jar
battery charged with thirty turns of his machine. By this means he
was able to estimate that a small battery which decomposed a grain of
water, furnished as much electricity as 800,000 discharges of his large
Leyden battery, and would form a powerful stroke of lightning, if dis-
charged at once.

The investigation gives us the first rough idea of the magnitude of the
quantities involved in frictional and voltaic electricity, and it may be
considered as the first rough approximation to the ratio of the electro-
magnetic to the electrostatic units of electricity.

But Faraday was a chemist. His associations with Davy had made
Tii-m familiar from the first -wi-th the chemical action of the battery, and
it is but natural that his attention should be directed to its investigar
tion. In the progress of these researches he noted the curious fact that
all bodies which could be decomposed by electricity when a fluid, could
neither conduct the current nor be decomposed by it when they were
solidified by the cold. The conduction and decomposition went to-
gether. Eising from this to a general law, he finally proved, by im-
mense labor, that, for a given quanti-ty of electricity, whatever the de-
composing conductor may be, the amount of chemical action is the
same. The current, the size of the electrodes and the strength of the
solution might vary, but the amount decomposed by a given quantity of
electricity remained the same. FuTthermore, the amount oP difforont
substances separated was in proportion to their chemical equivalents.
Hence, the voltameter for measuring the electric currents which, in
the form of the silver voltameter, is to-day one of our most accurate in-
struments.

As I have mentioned before, the leading idea in Faraday’s mind was
the replacing of all action at a distance by curved linos of force which
had a definite physical existence. So, in attacking this subject of elec-
trolysis, he very quickly showed that Davy’s idea that the poles sepa-
rated an electrolyte, by actually attracting its coinpommts, wivs false,
and that the theory, according to which decomposition and recompo-
sition took place throughout the whole course of the current in the elec-
trolyte, was correct.

Elecjtkioal and Magnetic Discoveries op Tabaday 645

Faraday now took up au analogous subject — ^the source of the elec-
tricity in the voltaic battery. He showed that the current from the
battery was proportional to the amount of zinc dissolved, and that the
direction of the current depended on the direction of the chemical
action.

The theory of Volta, that the contact of two metals was the source of
electricity, was thus elfeetuaUy disposed of, so that even the recent at-
tempt to revive that ancient theory could only have met with the disas-
ter which befell it.

It is impossible for me, in a few minutes, to give account of all that
Faraday did on these subjects of electrolysis and the tlieory of the voltaic
battej^. His work is a perfect mine of results — ^not haphazard and dis-
coimected, but each designed to elucidate some point in theory or dom-
onstrate some law, and his name must forever be associated with this
subject. His law of the definite chemical action of the current will
always form an enduring monument to his fame.

Every discovery that Faraday made only served as a guide to him in
making fresh ones.

"We have seen that Faraday found that when an electrolyte was in the
solid state it no longer conducted the current. To most cebservers this
would only have been an interesting, but disconnected, fact. But the
far-sighted mind of Faraday perceived in this an eaplanation of no less
a subject than that of electric induction. As in the electrolyte, he con-
ceived the particles to be arranged in certain directions, decomposing
and recomposing along lines in the direction of the electric currents, so
in the solidified electrolyte there was some arrangement along the lines
in which the current wished to pass, that is, of oloctric force. Hence his
theory of the nature of electric induction and of electric force. It was
not action at a distance, but the action of contiguous particles on each
other. As in magnetism, so in electricity, the action was carried to a
distance hy a medium.

Hot content with merely giving tho theory, ho proceeded to prove
it. If it were true, then the nature of tho medium should affect the
amount of the induction. Wo all know his beautiful apparatus for test-
ing this — ^the two globular Leyden jars which could be filled with
air, glass, oil of turpentine, gases, etc., how he divided the charge of
O'ne between the two and measured it on a Coulomb electrometer, and
thus discovered that his inference was correct, that each substance had
a specific inductive capacity, and that the charge of a condenser de-
pended not only on the area of the surface and tho thickness of the

646

BQEiTEy A. Eowland

diGlGctriCj tut also on the uatuiG of tliG lattor, air or vacuum producing
the least condensing effect, and glass, sulphur, etc., a greater one.

To complete his mental vision of an electrified system, it vras neces-
sary for him to test in a very complete manner the idea that positive
and negative electricities are generated in equal quantities. To accom-
plish this, he erected a roo-m of twelve feet on a side out of a frame-
work covered with tinfoil, and the whole insulated. By generating
electricity inside of it, he was able to prove in a more complete manner
than had been done before that we never generate positive electricity or
negative electricity by itself, but always in equal quantities together.
Every complete electrostatic system contains equal quantities of posi-
tive and negative electricity, which are separated by a dielectric, through
which they are connected by the lines of electric induction, whose ten-
sion produced electric attraction.

To-day, when the mathematics of Maxwell have added clearness to the
subject, we see every electrostatiG system made up of minute and equal
portions of positive and negative electricity, connected together by
tubes of induction as by elastic bands, these tubes repelling each other
laterally, so as to be held in position, we know that the attraction of all
electrified bodies is accounted for by such a system, which was roughly
conceived by Ifaraday, but in which the positions and form of every lino
can now be calculated.

It is impossible, on the present occasion, to follow Faraday through
all his researches on the different forms of electric discharge, and his
uiontinued researches on electrolysis; hut I will pass immediately to two
of his greatest discoveries, the action of magnetism on light and diamag-
netism. In his researches on optical glass he had discovered a variety of
heavy glass, called silicated borate* of lead. On placing this between
the poles of a magnet^ and looking through it along the lines of force,
he found that the plane of polarization was rotated.

Using other substances, he found that most of them liad some effect
of this kind in the magnetic field. The laws of the magnetic rotation
he found very different from those of the ordinary rotation of turpen-
tine or sugar, and altogether it forms a most interesting and important
experiment when considering the theorj’^ of magnetism.

Ifot content with discovering this law with his piece of optical glass,
he now sought to discover whether there was any force of attraction
or repulsion between it and the magnet. Hanging it up between the
poles, he discovered that as iron was attracted by a magnet, so the heavy
glass was repelled. He called this property diamagnetism, and showed

Elbotbical and Magnbtio Disoovbeies OB Pabadat 64'}'

that all bodies were acted upon by magnetism and could be classified as
magnetic or diamagnetic. Magnetism now had a univeisal significance
as applying to all bodies. It was universal in its action, and all bodies
responded to it to some extent at least. Even gases wore acted on by it,
and the oxygen of the air was found quite strongly magnetic.

Quickly his mind seized another idea.

As the intense magnetism of iron, nickel and cobalt was destroyed by
heat, might it not be possible that all bodies should become magnetic
when cold? He carefully tried the experiment, but never was able to
find any effect with the means of producing cold at his command.

In reading Paraday’s papers we are surprised at the clearness vith
which his laws arc expressed. Although he naturally wished to bring
his lines of force into use in this case of diamagnetism, yet we now find
him making no use of them. His law says that magnetic substances in
the field of a magnet tend to the stronger part of the field, and the dia-
magnetic to the weaker, irrespective of the direction of the linos of
force.

Bismuth he found the most strongly diamagnetic of all bodies. In
using a crystal of this substance instead of a bar, he found that it
would set itself in a magnetic field, even if this was uniform. On using
other sxibetances he proved the general law that all crystals possessed
this property and he called it magne-crystallic force.

The researches on diamagnetism and magne-ciystallic force occupied
Faraday’s time for five years, from 1846 to 1860, and he was now in the
sixtieth year of his age. Ho more great discoveries fell to his lot, but
his mind turned more and more to brooding over the consequences of
his past discoveries and following out their results.

Ihe idea of lines of force was still on his mind, and the discovery of
diamagnotisra had now given him a further insight into their nature.
He saw that the magnetic and diamagnetic nature of iKxlies could be
explained by considering them as good or bad conductors of these lines
of force. Iron was a good conductor and bismuth a bad one. Wlxen
soft iron was placed in a magnetic field, the lines of force, or, as we now
more exactly term them, the lines of induction, were more easily con-
ducted by it than by the air, and they were deflected toward and through
it; but a piece of bismuth was a poorer conductor and these lines of
force tended to pass around it rather than through it. By surrounding
a weak magnetic body by a strong magnetic fluid he found that it pos-
sessed all the properties of a diamagnetic one. Pxtrsuing the subject,
he showed how the lines of induction wore distributed around and within

648

Henet a. Eowland

a magnet, and hov we are able to measure them by the induced current
in moving wires. The method of exploring the magnetic field is the only
exact method which has ever been devised for nse in such cases as the
field of modem dynamo-electric machines, or in most of the problems
of modem electrical engineering. He also proved that the lines of in-
duction are always closed chenits, whether they axe due to permanent
magnets or electric currents, thus forever destroying onr ho*pe of obtain-
ing a continuons current by induction without tiie use of a commutator.

When a soft iron bar was approached to the magnet, it drew the lines
in upon itself; they proceeded down the bar until they were forced into
the badly conducting air and the number which went further down the
bar to those which passed out into the air at any point was in proportion
to the conductivity of the two. A steel magnet was, in his eyes, lilce a
voltaic pile in water. As the current of electricity was forced forward
hy the electromotive force of the pile and diffused itself in currents
through the water^ so the lines of magnetic induction were formed by
the coercive power of the steel. It is now known to he a fact th.at the
distribution of magnetism on a steel magnet, or indeed in any case, can
be calculated by these principles Faraday laid down. The idea of a inag-»
netie circuit is familiar now to all electrical engineers.

To Faraday^s eye, a magnet not only consisted of a piece of steel or
loadstone whidi is apparent to our ordinary vision, but included all the
space around which was filled with Knes of force; it was bounded only by
the limits of the universe. The steel served merely to bind together
the ring-like lines of induction which passed from the magnet to every,
point of space.

Faraday was not a mathematician, and could not thus follow out the
consequences of his great ideas. This has been done for him by the im-
mortal Maxwell. He has taken up the idea that electrical and mag-
netic forces only proceed to a distance by aid of the intervening particles
of matter, or ether, as the case may be, and has given it a mathematical
basis.

To-day a body charged with electricity, a magnet or a wire carrying
an electrical current, all are inco-mplete without the space around tlioin.

When we attach a battery to a wire and the current apparently flows
through it aa if it were a current of water, Faraday's idea shows us that
we are only looking at the matter superficially; around that wire and
permeating space in every part are lines of magnetic force, and linos of
electrostatic force. At the moment of joining the battery to the wire
this whole complicated system of lines of force must be formed. At the

Eleotkeoal and IMagnetio Dmogyeeies of Faradat 649

moment of breaking circuit, the system must yanish, and we obtain the
energy stored up in this space surroundiag the wire in the bright spark
known as the extra current.

What a flood of light this throws on many experiments such as those
of Wheatstone, on the velocity of electricity. With his wire arranged
in parallel loops around an ordinary room, he discharged a Leyden jax
through it, and assumed that the electricity passed through the whole
wire before a spark could form at the distant end. But we know that
whole room was instantly filled with moving lines of magnetic force,
which induced currents in every wire they crossed, and hence what
Wheatstone measured was merely the current induced from one wire
or those near it.

Thomson and Maxwell have shown that the medium around a wire
carrying an electric current is in motion, and that the vortex filaments
form Earaday^s lines of magnetic force; for Faraday^s discovery of the
magnetic rotation of the plane of polarization of light can be explained
in no other way.

Thus the discoveries of Faraday have been engrafted on our science,
and form one of its most essential features. They are among the foun-
dation stones of the edifice of our science.

We know far more than the electricians of that day, in the details of
the subject, and mathematics has given us a broad view of electricity
and magnetism, such as never before was obtained. In its practical use
and measurement we have made immense strides in devising methods
and instruments, and we now cany out our experiments on a scale which
Faraday could not attempt, seeing that subject, which has hitherto boon
best adapted to the contemplation of a few philosophers, has become
of use to all, and electricity bids fair to become our most important
servant.

The spark, which Faraday more than fifty years ago observed in a
darkened room, now blazes out almost vrith the power of the sim, but it
is still the spark of Faraday. Though it is a thousand times as large, it
is still made on the principles which Faraday laid down, and nothing
except mechanical details has ever been added to- its process.

How suitable, then, that we should remember his name on this
occasion, since hia discoveries have served as the basis of all progress
in electrical engineering. Had Faraday not lived we should not have
been here to-night. True, as I have shown before, the progress of science
could only have been delayed by the absence of any one man, but how
long, in this case, we cannot tell. We can only receive with gratitude

650

Hhnkt a. Rowland

what Faraday haa given freely to us, and speak his name witli the rever-
ence due, not only to his intellectual eminence, but to his character.
Too noble to leave science for the wealth held out to him, he persevered
in it to the end, and gave to. the world the fruits of his labor in his
‘Experimental Researches in Electricity.’

He never obtained from the world the material reward for his labor,
but died a poor man, who had enriched the world.

¥e stand at an important epoch in the history of our science. We
have gone far enough into its practical applications to see some dis-
tance into the future. The arc lights which Davy brought into promi-
nence at the beginning of this century, fed by the machines of Faraday,
blazes throughout the night in all cities of the world. The incandescent
light, known long to scientists, has been improved and bids fair to rival
gas in cheapness, as it surpasses it in beauty. The secondary battery
discovered by Ritter eighty years or more ago, improved by Plants and
Paure in recent times, stiR struggles to fill the place assigned to it, to be
replaced by one before long which shall not waste fifty per cent of the
power given to i^ and weigh tons for a few foot-pounds of energy stored
up. We see it in its new form replacing the laboring horses in the
streets, and serving in many cases where small power is needed. But the
transmission of energy seems to me to open one of the widest fields, and
the time is not very distant when a few large engines will replace the
numerous small ones in our cities; when also the power of waterfalls may
be made available at a distance.

The principle of the telephone also is destined to bear unseen fruit.

There is work for all, the practical and theoretical man nhVg

The philosopher, studying the problems of the universe, deems himself
rewarded by some new fact discovered, some new law demonstrated. To
him the universe is a problem to solve, and his motto is, “ Science is
knowledge.”

He sees before him the time when man’s insight into nature shall be
vastly increased, and esteems the science of to-day as but an atom to
what we shall know in the future. 'While not despising the wealth, he
seldom has time for its accumulation, as he considers other things of
vastly more importance; the truth is what he seeks; the truth as to this
wonderful universe in which we live. What is matter? what is electric-
ity, what is the medium which transmits light from one point to an-
other, how comes it that the earth is magnetic? These are some of the
problems he is trying to solve. He knows that one man can do but little
toward it, even though he should surpass what Faraday has done, but

Elboteioal and Magnetic Discoveries ot Faraday 651

he trusts to the combined eflEo-rts of mankind, shown in the steady prog-
ress of science, to finally arrive at a solution.

The devotee o-f applied science, the so-called practical man, looks
upon the forces of nature as his servants, and strives to become their
master. The world must move, its work must be accomplished. We
are not satisfied to live as our fathers have done, and we must have
luxuries unknown to them. Our thoughts must fly to the fartliest parts
of the earth in an instant, at our bidding, and we must pass from point
to point on the wings of the wind, for flesh and blood is too slow for us.
To accomplish this, the engineer harnesses the forces of nature and
compels them to work for Mm. He takes the discoveries of the phil-
osopher and uses them for the practical needs o-f daily life. His motto
is, Science is power As he ministers more directly to the present
generation of mankind than to the generations to come, as does the phil-
osopher, so he often reaps Ms reward in the present, and retains some
of that wealth which his inventions bring into the world. For the
source of the wealth of the world is labor, and the labor of the forces
of nature, in our behalf, surpasses very many fold that of human flesh
and blood. He who adds but the slightest to our power over these
forces enriches the world, and is entitled to its practical, as well as its
sentimental gratitude, be he philosopher or engineer. The great ques-
tion which we should ask ourselves is how our science can best be fur-
thered. The philosopher must precede the engineer. To have the ap-
l)lications of electricity, there must be a science of electricity. This
science cannot depend for its existence on practical men whose minds
are engrossed with other than theoretical problems. It must exist in
minds like Faraday, which are specially adapted to its reception and
advancement — men who are willing to* devote their lives to it, and who
have the ability to further it. We cannot create such men, but we can
give them our practical as well as our sentimental sympathy, when
found. The pMlosopher is made of flesh and blood as well as other
men. He must live and have his tastes gratified as well as others.
His place in the world as at present constituted is usually that of a pro-
fessor in our universities and colleges. Are only men like Faraday
chosen for these positions? Of the four hundred or more, how many
choose their professors on account of their eminence in theoretical
science? Are there a do^ien? I doubt it. Furthermore, what facilities
and encouragement would they have in those institutions to do work?
Too far away from each other to ])e a mutual help, they have but an
incomplete scientific life. Faraday could not have been himself in

652

Henet a. Eowlan-d

Africa and vonld have languished in onr own conntiy. In London, in
contact with the science of Europe and encouraged by its atmosphere,
with the Eoyal Society at which to announce his discoveries and the
Eoyal Institution in which to make them, Faraday, in spite of poor
education, was stimulated to his best efforts. Alone in one of our iso-
lated colleges, cut off from intercourse with the rest of the world by a
so-called protective duty on his very life, boots, with no journal spe-
cially devoted to theoretic physics, and no society like the Eoyal Society,
who can say whether his discoveries would have been made or not? The
endowment of research seems to me to offer the best means out of the
difficulty. Let professorships be endowed and funds to pay the expenses
of apparatus and assistants be formed in our universities, with the under-
standing that the research is to be the principal work; work, while teacli-
ing is not to be neglected. The result will be the formation of a scien-
tific atmosphere in which men like Faraday can live and labor, and the
dry bones of the pedagogue be replaced by the fire and life of the orig-
inal investigator. And let not practical science be neglected. Let us
have scientific schools of the highest grade, where modern science is
taught, so that fifty years shall not again pass, as it has done, before a
discovery like that of Faraday is utilized.

Furthermore, let us have scientific societies and clubs like the pres-
ent, where men of like tastes can meet and interchange ideas.

Thus we meet together to-night, electricians all, practical and theo-
retical, at a time in the history of our science and of the world which
will in future he called the begiuning of the age of electricity.

The feeble attraction of the amber has become a mighty force, which
is destined to make itself felt, and it is to be hoped that onr mutual in-
tercoxmse in this Club may aid us all in our efforts to make an impress
on its future bistory.

ON MODEEN VUVS WITH EESPBCT TO ELECTRIC
CURRENTS

ADDBBB8 BBFOBB THB AMBBIOAN lirSTXl^tTTB OF BLBOTBIOAL SNGIBBBBB,

WHW 70BK, MAY 23, 1889

ITramactiofu of the American Inetitute of Electrical Engineer e^ VI, 842-857, 1889J

Ab, a short time since, I stood in a library of scientific books and
glanced axo-und me at the works of the great masters in physics, my mind
wandered back to the time when the apparatus for a complete course
of lectures on the subject of electricity consisted of a piece of amber
and a few light bodies to be attracted by it From that time until
now, when we stand in a magnificent laboratory with elaborate and
costly apparatus in great part devoted to its study, how greatly has the
world changed and how our science of electricity has expanded both in
theory and practice until, in the one case, it threatens to include within
itself nearly the whole of physics, and in the other toi make this the age
of electricity.

Were I to trace the history of the views of physicists with respect
to electric currents it would include the whole history of electricity.
The date when the conception of an electric current was possible was
when Stephen Gray, about 170 years ago, first divided bodies into con-
ductors and non-conductors, and showed that the first possessed the
property of transmitting electrical attractions to a distance. But it
was only when the Leyden jar was discovered that the idea of a current
became very definite. The notion that electricity was a subtle fluid
which could flow along metal wires as water flows along a tube, was
then prevalent, and, indeed, remains in force to-day among all ex-
cept the leaders in scientific thought It is not my intention to depre-
ciate this notion, which has served and still serves a verj^ important pur-
pose in science. But, for many years, it has been recognized that it in-
cludes only a very small portion of the truth and that the mechanism by
which energy is transmitted from one point of space to another by means
of an electric current is a very complicated one.

Here for instance, on the table before me are two rubber tubes filled
with water, in one of which the water is in motion, in the other at rest.
It is impossible, by any means now known to us, to find out, without
moving the tubes, which one has the current of water flowing in it and

654 :

Hbnky a. Eowlan-d

■which has 'the water at rest. Again, I ha\e here two wires, alike in all
respects, except that one has a current of electricity flowing in it and
the other has not. But in this case I have only to bring a magnetic
needle near the two to find out in which one the cnrrent is flowing. On
our ordinary sense the passage of .the current has little effect; the air
around it does not turn green or the wire change in appearance. But
we have only to change our medium from air to one containing magnetic
particles to perceive the commotion which the presence of a current
may cause. 'Thus this other wire passes through the air near a large
number of small suspended magnets, and, as I pass the current through
it, every magnet is affected and tends to turn at right angles to the wire
and even to move toward it and -wrap itself around it. If we suppose
the number of these magnets to become very great and their size small,
or if we imagine a medium, every atom of which is a magnet, we see that
no wire carrying a current of electricity can pass through it without
creating the greatest commotion. Possibly this is a feeble picture of
what takes place in a mass of iron near an electric current.

Again, coil the wire around a piece of glass, or indeed, almost any
transparent substance, and pass a strong current through the wire.
With our naked eye alone we can see no effect whatever, as the glass is
apparently unaltered by the presence of the current; but, examined in
the proper way, by means of polarized light, we see that the structure of
the glass has been altered throughout in a manner which can only be
explained by the rotation of something within the glass many millions
of times every second.

Once more, bring a wire in which no current exists nearer and nearer
to the one carrying the current, and we shall find that its motion in such
a neighborhood causes or tends to cause an electric current in it. Or, if
we move a large solid mass of metal in the neighborhood of such a cur-
rent we find a peculiar resistance unfelt before, and if we force it into
motion we shall perceive that it becomes warmer and warmer as if there
was great friction in moving the metal through space.

Thus, by these tests, we find that the region around an electric cur-
rent has very peculiar properties which it did not have before, and
which, although stronger in the neighborhood of the current, still ex-
tend to indefinite distances in all directions, becoming weaker as the
distances increase.

How great, then, the difference between a current of water and a cur-
rent of electricity. ' The action of the former is confined to the interior
of the tube, while that of the latter extends to great distances on all

Modebn Views with Ebbpeox to Elboteio Ctthbents 666

sides, the whole of space being agitated by the fonnatioa of an electric
current in any part. To show ^s agitation, I hare hei-e two large
frames with coils of wire around them. They hang face to face about
6 feet apart. Through one I discharge this Leyden jar, and immediately
you see a spark at a break in the wire of the other coil, and yet there is
no apparent connection between the two. I can cany the coils 60 feet
or more apart, and yet by suitable means I can obserre the disturbances
due to the current in the first coil.

The question is forced upon us as to how this action takes place. How
is it possible to transmit so much power to such a distance across appar-
ently unoccupied space? According to our modem theory of ph 3 rsics
there must be some medium engaged in this transmission. We know
that it is not the air, because the same efiects take place in a vacuum,
and, therefore, we must fall back on that medimn which transmits light
and which we have named the ethei-. That medium which is supposed
to extend unaltered tiiroughout the whole of space, whose existence is
very certain but whose properties we have yet but vaguely conceived.

I cannot^ in the course of one short hour, give even an idea of the
process by which the minds of physicists have been led to this conclusion
or the means by which we have finally completely identified the ether
which transmits light with the medium which transmits electrical and
magnetic disturbances. The great genius who first identified the two is
Maxwell, whose electro-magnetic theory of light is the centre around
which much scientific thought is to-day revolving, and which we regard
as one of the greatest steps by which we advance nearer to the under-
standing of matter and its laws. It is this great discovery of Maxwell
which allows me, at the present time, to attempt to explain to you the
wonderful events which happen everywhere in space when one estab-
lishes an electric current in any other portion.

In the first place, wo discover that the disturbance docs not take place
in all portions of space at once, but proceeds outwards from the centre
of the disturbance with a velocity exactly equal to the velocity of light.
So that, when I touch these wires together so as to complete the circuit
of youder battery, I start a wave of ethereal disturbance which passes
outwards with a velocity of 185,000 miles per second, thus reaching the
sun in about eight minutes, and continues to pass onwards forever or
until it reaches the bounds of the universe. And yet none of our senses
inform us of what has taken place unlc*ss wo sharjicn thorn by the use of
suitable instruments. Thus, in the case of these two coils of wire, sus-
pended near each other, which we have already used, when the wave

656

Heitet a. Eowland

from, the primary disturhance reaches the second coil, we perceiTe the
disturbance by means of the spark formed at the break of the coil.
Should I moye the coils farther apart, the spark in the second coil would
be somewhat delayed, but the distance of 185,000' miles would be neces-
sary before this delay could amount to as much as one second. Hence
the efiEeets we observe on the earth take place so nearly instantaneously
that the interval of time is yery difficult to measure, amounting, in the
present case, to only Ty oT roV oD O ' ^ second.

It is impossible for me to prove the existence of this interval, but I
can at least show you that waves have something to do with the action
here observed. For instance, I have here two tuning forks mounted on
sounding boxes and tuned to exact unison. I sound one and then stop
its vibrations with my hand, instantly you hear that the other is in vibra-
tion, caused by the waves of sound in the air between the two. When,
however, I destroyed the unison by fixing this piece of wax on one of the
forks, the action ceases.

ITow, this combination of a coil of wire and a Leyden jar is a vibrating
system for electricity and its time of vibration is about 10,000,000
times a second. This second system is the same as the first, and there^
fore its time of vibration is the same. You see how well the experiment
works now because the two are in unison. But let me take away this
second Leyden jar, thus destroying the unison, and you see that the
sparks instantly cease. Eeplacing it, the sparks reappear. Adding an-
other on one side and they disappear again, only to reappear when the
system is made symmetrical by placing two on each side.

This experiment and that of the tuning forks have an exact analogy
to one another. In each we have two vibrating systems coimected by a
medium capable of transmitting vibrations, and they both come under
the head of what we know as sympathetic vibrations. In the one case,
we have two mechanical tuning forks connected by the air; in the other,
two pieces of apparatus which we might call electrical tuning forks, con-
nected by the luminiEerous ether. The vibrations in one case can be
seen by the eye or heard by the ear, but iu the other case they can only
be perceived when we destroy them by making them produce a spark.
The fact that we are able to increase the effect by proper tuning dem-
onstrates that vibrations are concerned in the phenomenon. This can,
however, be separately demonstrated by examining the spark by means
of a revolving mirror, when we find that it is made up of many succes-
sive sparks corresponding to the successive backward and forward move-
ments of the current.

MoDERi^r Views with Respect to Eleotbic Currents 667

The fact of the oscillatory character of the Lfeyden. jar discharge was
first demonstrated by our own comtryman, Henry, in* 1832, but he pur-
sued the subject only a short distance, and it remained for Sir "Williaiii
Thomson to give the mathematical theory and prove the laws according
to which the phenomenon takes place.

Thus, in the case of a charged Leyden jar whose inner and outer coat-
ings have been suddenly joined by a wire, the electricity flows back and
forth along the wire until all the energy originally stored up in the jar
has expended itself in heating the wire or the air where the spark takes
place and in generating waves of disturbance in the ether which move
outward into space with the velocity of light. These ethereal waves we
have demonstrated by letting them fall o-n this coil of wire and causing
the electrical disturbance to manifest itself by electric sparks.

I have here ano-ther more powerful arrangement for producing electro-
magnetic waves of very long wave-length, each one being about 500
miles long. It consists of a coil, within which is a bundle of iron wires.
On passing a powerful alternating can*ent through the coil, the iron
wires are rapidly magnetized and demagnetized, and send forth into
space a system of electro-magnetic waves at the rate of 360 in a second.

Here, also, I have another piece of apparatus [a lamp] for sending
out the same kind of electro-magnetic waves; on applying a match, we
start it into action. But the last apparatus is tuned to so high a pitch
that the waves are only -yyjTnr 55,000,000,000,000 are

given out in one second. These short waves are known by the name of
light and radiant heat, though the name radiation is more exact. Plac-
ing any body near the lamp so that the radiation can fall on it, we ob-
serve that when the body absorbs the rays it is heated by them; the
well-known property of so-called radiant heat and light. Is it not pos-
sible for us to get some substance to absorb the long waves of disturb-
ance, and so obtain a heating effect? I have liere such a substance in
the shape of a sheet of copper, which I fasten on the face of a thermo-
pile, and I hold it where the waves are the strongest [near the coil while
the alternating current is passing through it]. As I have anticipated,
great heat is generated by their absorption, and soon the plate of copper
becomes very warm, as we see by this thermometer, by feeling it with
the hand, or even hy the steam from water thrown upon it. In this ex-
periment the copper lias not touched the coil or tho iron wire core,
although if it did they are very much cooler than itself- The heat has
been produced by the absorption of the waves in the same way as a
42

668

Heney a. Eowland

blackened body absorbs the rays of shorter wave-length from the lamp;
and, in both cases, heat is the result,^

But in this experiment, as in the fLrst one, the wave-like nature of the
disturbance has not been proved experimentally. We have caused elec-
tric sparks, and have heated the copper plate across an interval of space,
but have not in either of these cases proved experimentally the progres-
sive nature of the disturbance; for a ready means of experimenting on
the waves, obtaining their wave-length and showing their interferences,
has hitherto been wanting. This deficiency has been recently overcome
by Professor Hertz, of Carlsruhe, who has made a study of the action of
the coil, and has shown us how to use it for experiments on the ethereal
waves, whose existence had before been made certain by the mathemat-
ics of Maxwell.

I scarcely know how to present this subject to a non-technical audience
and make it clear how a coil of wire with a break in it can be used to
measure the velocity and wave-lengths of ethereal waves. However, I
can but try. If the waves moved very slowly, we could readily measure
the time tiie first coil took to afiect the second, and show that this time
was longer as the distance was greater. But it is absolutely inapprecia-
ble by any of our instruments, and another method, must be found. To
obtain the wave-length Professor Hertz used several methods, but that
by the formation of stationary waves is the most easily grasped. Mr.
Ames holds in his hand one end of a spiral spring, which makes a very
heavy and flexible rope. As he sends a wave dovm it, you see that it is
reflected at the further end, and returns again to his hand. If, how-
ever, he sends a succession of waves down the rope, the reflected waves
interfere with the direct ones, and divide the rope into a succession of
nodes and loops, which you now observe. So a series of sound waves,
striking on a wall, form a system of stationary waves in front of the wall.
With this in view, Professor Hertz established his apparatus in front of
a reflecting wall, and observed the nodes and loops by the sparks pro-
duced in a ring of wire. It is impossible for me to repeat this experi-
ment before you, as it is a very delicate one, and the s]mrka produced are
almost microscopic. Indeed, I should have to erect an entirely differ-
ent apparatus, as the waves from the one before me are nearly i mile
long, the time of vibration of the system being very great, that is
TgTif u 0 0 0 of a second. To produce shorter waves we must use appa-

^The thermopile was connected with a delicate mirror galyanometer, the de-
flections of which were shown on a screen.

Modben Views with Eespbot to Edeotbio Cueeints 659

ratus tuned, as it were, to a higher pitch, in which the same principle is,
however, employed, but the ethereal waves are shorter, and thus several
statio-nary waves can be contained in one room.

The testing coil is then moved to different portions of the room, and
the nodes are indicated by the disappearance of the sparks, and the
loops by the greater brightness of them. The presence o-f stationary
waves is thus proved, and their half wave-length found from the dis-
tance from node to node, for stationary waves can always be considered
as produced by the interference of two progressive waves advancing in
opposite directions.

However interesting a further description of Professor Hertzes experi-
ments may be, we have gone aa far in that direction as our subject car-
ries us, for we have demonstrated that the production of a current in a
wire is accompanied by a disturbance in the ' surrounding space; and,
although I have not experimentally demonstrated the ethereal waves, yet
I have proved the existence of electric oscillations in the coils of wire
and the ether surrounding it.

Our luatliematics has demonstrated, and experiments like those of
Professor Hertz have confirmed the demonstration, that the wave dis-
turhancG in the ether is an actual fact.

The closing of a battery circuit, then, and the establishment of a cur-
rent of electricity in a wire is a very different process from the forma-
tion of a current of water in a pipe, though, after the first shock, tho
laws of the flow of the two arc very much alike. But even then, the
medium around the current of electricity has very strange properties,
showing that it is accompanied by a disturbance throughout space. The
wire is but tho core of the disturbance, which latter cxtoncls indefinitely
in all directions.

One of the strangest things about it is that wc can calculate with per-
fect exactness the velocity of the wave propagation and tho auiount of
the disturbance at every point and at any instant of time; but as yot we
cannot conceive of the details of the mechanism which is concernod in
the propagation of an electric cuiTcnt. In this respect our subject n.^scin-
bloR all other branches of physics in the partial knowledge wo have of it.
We know that light is the undulation of the luminiferous other, and yot
the constitution of the latter is unknown. Wo know that tho atoms of
matter can vibrate with purer tones than the most perfect piano, and
yet wo cannot even conceive of their constitution. We know that the
sun attracts the planets with a force whoso law is known, and yet we
fail to picture to ourselves tho process by which it takes our earth within

660

Hbnet a. EowLAin)

its grasp at the distance of many millions of miles and prevents it from
departing forever from its life-giving rays. Science is full of this half
knowledge, and the proper attitude of the mind is one of resignation
toward that which it is impossible for us to know at present and of ear-
nest striving to help in the advance of our science, which shall finally
allow us to answer all these questions.

The electric current is an unsolved mystery, but we have made a very
great advance in understanding it when we know that we must look out-
side of the wire at the disturbance in the medium before we can under-
stand it: a view which Faraday dimly held fifty years ago, which was
given m detail in the great work of Maxwell, published sixteen years
since, and has been the guide to most of the work done in electricity
for a very long time. A view which has wrought the greatest changes
in the ideas which we have conceived with respect to all electrical
phenomena.

So far, we have considered the case of alternating electric current in
a wire connecting the inner and outer coatings of a Leyden jar. The
invention of the telephone, by which sound is carried from one point to
another by means of electrical waves, has forced into prominence the
subject of these waves. Furthermore, the use of alternating currents
for electric lighting brings into play the same phenomenon. Here,
again, the difference between a current of water and a current of elec-
tricity is very marked. A sound wave, traversing the water in the tube,
produces a to and fro current of water at any given point. So, in tlio
electrical vibration along a wire, the electricity moves to and fro along
it in a manner somewhat similar to the water, but with this difference: —
the disturbance from the water motion is confined to the tube and the
oscillation of the water is. greatest in the centre of the tube, while, in
the ease of the electric current, the ether around the wire is disturbed,
and the oscillation of the current is greatest at the surface of the wire
and least in its centre. The oscillations in the water take place in the
tube without reference to the matter outside the tube, whereas tlic elec-
tric oscillations in the wire are entirely dependent on the surrounding
space, and the velocity of the propagation is nearly independent of the
nature of the wire, provided only that it is a good conductor.

We have, then, in the case of electrical waves along a wire, a disturb-
ance outside the wire and a current within it, and the equations of
Maxwell allow us to calculate these with perfect accuracy and. give all the
laws with respect to them.

We thus find that the velocity of propagation of the waves along a

Modbbk Views with Eespeot to Eleotbio Cttebehts 061

wire, himg far away from other bodies and made of good conducting ma-
terial, is that of light, or 185,000 miles per second; but when it is
hung near any conducting matter, like the earth, or inclosed in a cable
and sunk into the sea, the -velocity becomes much less. 'When hung in
space, away from other bodies, it forms, as it were, the core of a system
of waves in the ether, the amplitude of the disturbance becoming less
and less as we move away from the wire. But the most curious fact is
that the electric current penetrates only a short distance into the wire.

Diaouam 1.

being mostly confined to the surface, especially where tlie number of
oscillations per second is very great.

The electrical waves at the surface of a conductor are thus, in some
respects, very similar to the waves on tlie surface of the water. The
greatest motion in the latter case is at the surface, while it diminishes
as we pass downward and soon becomes inappreciable. Furthermore,
the depth to which the disturbance penetrates into the water increases
with increase of the length of the wave, being confined to very near the
surface for very short waves. So the disturbance in the copper pene-
trates deeper as the waves and the time of oscillation are longer, and the
disturbance is more nearly confined to the surface as the waves become
shorter. I have recently made the complete calculations with respect

662

Hbney a. Eowland

to these wayes, and have drawn some diagrams to illustrate the penetra-
tion of the alternating current into metal cylinders. Tlie first diagram
represents the ciirrent at different depths in a copper cylinder, 45 cm.
diameter, or an iron one 144 cm, diameter, traversed by an alternating
current with 200 reversals per second. The first and second curves
show us the current at two different instants of time, and sliow us how
the phase changes as we pass downward into the cylinder. By reference
to the third curve we see that it may be even in the opposite direction in
the centre of the cylinder from what it is at the surface. The third
curve gives us the amplitude of the current oscillations at different
depths irrespective of the phase, and it shows us that the current at the

centre is only about 10 per cent of that at tlie surface in this case. The
second diagram shows us the distribution in the same cylinders when the
number of reversals of the current is increased to 1800 per second. Hero
we see that the disturbance is ahnost entirely confined to the surface, for
at a depth of only 7 mm. the disturbance almost entirely vanishes.

There are very many practical applications of these theoretical results
for electric currents. The most obvious one is to the case of conductors
for the alternating currents used in producing the electric light. Wc
find that when these ai’e larger than about half an inch diameter they
should be replaced by a number of conductors less than lialf an inch
diameter, or by strips about a quarter of an inch thick, and of any con-
venient width. But this is a matter to be attended to by the elec?tric
light companies-

Prof. Oliver J. Lodge has recently, in the British Association, drawn

Hobeknt Views with Respect to Eleotkic Citbeents 663

attention to the application of these results to lightning rods. Alnaost
since the time of Franklin there haye been those who adyocated the
making of lightning rods hollow, to increase the surface for a giyen
amount of copper. We now know that these persons had no reason for
their belief, as they simply drew the inference from the fact that elec-
t]*ieity at best is on the surface. ISTeither were the adyocates of the solid
rods quite correct, for they reasoned from the fact that electricity in a
state of steady flow occupies the whole area of the conductor equally.
The true theory, we now know, indicates that neither party was entirely
correct and tliat the surface is a yery important factor in the case of a
current of electricity so sudden as that from a lightning discharge. But
increase of surface can best be obtained by multiplying the number of
conductors, rather than making them flat or hollow; and, at the same
time, Maxweirs principle of enclosing the building within a cage can he
carried out. Theory indicates that the current penetrates only one-
tenth the distance into iron that it does into copper. As the iron has
seven times the resistance of copper, we should need 70 times the sur-
face of iron that we should of copper. Hence I prefer copper wire
about a quarter of an inch diameter and nailed directly to the house
without insulators, and passing down the four corners, around the eaves
and over the roof, for giving protection from lightning in all cases where
a metal roof and metal down spouts do not accomplish the same purpose.

Whether the discharge of lightning is oscillatory or not docs not enter
into the question, provided it is only sufficiently sudden. I have re-
cently solved the mathematical problem of the electric oscillations along
a perfectly conducting wire joining two infinite and perfectly conducting
planes parallel to each other, and find tlmt there is no definite time o-f
oscillation, hut that the system is capable of vibrating in any time in
which it is originally started. The case of lightning between a cloud of
limited extent and the earth along a path through the air of great re-
sistance is a very different problem. Both the cloud and the path of the
oloctricity are poor conductors, which tends to lengthen the time. If I
were called on to estimate as nearly as possible what took place in a flash
of lightning, T would say that I did not bolievo that the discharge was
always oscillating, but more often consisted of one or more streams of
electricity at intervals of a small fraction of a second, each one continu-
ing for not less than ro oVoo second. An oscillating current with 100,000
reversals per second would pentetrate about 75 * 5 - inch into copper and rh
inch into iron. The depth for copper would constitute a considorable
portion of a wire ^ inch diameter, and, as there are other considerations

664

Hbnky a. Eowland

to be taken into account, I believe it is scarcely wortb while making
tubes, or flat strips, for such small sizes.

It is almost impossible to draw proper conclusions from experiments
on this subject in the laboratory such as those of Prof. Oliver J. Lodge.
The time of oscillation of the current in most pieces of laboratory ap-
paratus is so very small, being often the fo g ir i r o T r inr ^ ^ second, that
entirely wrong inferences may be drawn from them. As* the size of
the apparatus increases, the time of oscillation increases in the same pro-
portion, and changes the whole aspect of the case. I have given
of a second as the shortest time a lightning flash could proba-
bly occupy. I strongly suspect it is often much greater, and thus de-
parts even further from the laboratory experiments of Professor Lodge,
who has, however, done very much toward drawing attention to this
matter and showing the importance of surface in this case. All shapes
of the rod with equal surface are not, however, equally efldcient. Thus,
the inside surface of a tube does not count at all. Neither do the corni-
gations on a rod count for the full value of the surface they expose, for
the current is not distributed unifo-rmly over the surface; but I have
recently proved that rapidly alternating currents are distributed over the
surface of very good conductors in the same manner as electricity at
rest would be ^stributed over them, so that the exterior angles and cor-
ners possess much more than their share of the current, and eomiga-
tions on the wire concentrate the current on the outer angles and dimin-
ish it in the hollows. Even a flat strip has more current on the edges
than in the centre.

Pot these reasons, shape, as well as extent of surface, must be taken
into account, and strips have not always an advantage over wires for
quick discharges.

The fact that the lightning rod is not melted on being struck by
lightning is not now considered as any proof that it has done its work
properly. It must, as it were, seize upon the discharge and offer it an
easier passage to the earth than any other. Such sudden currents of
electricity we have seen to obey very different laws from continuous ones,
and their tendency to stick to a conductor and not fly off to other ob-
jects depends not only on haviug them of small resistance, but also on
having what we call the self-induction as small as possihlo. This latter
can be diminished by having the lightning rod spread sideways as much
as possible, either by rolling it into strips, or better, by making a network
of rods over the roof, with several connections to the earth at the corners,
as I have before described.

Modben Views with Eespeot to Elbotrio OxTREENrs 665

Thus we see that the theory of liglitniEg rods, which appeared so sim-
ple in. the time of Franklin, is to-day a very conaplicated one, and re-
quires for its solution a very complete knowledge of the dynamics of elec-
tric ciurents. In the light of our present knowledge the frequent fail-
ure of the old system of rods is no mystery, for I doubt if there are a
hundred buildings in the country properly protected from lightning.
With our modem advances, perfect protection might be guaranteed in all
cases, if expense were no object

So much for the rod itself, and now let us turn to other portions of
the electrical system, for we have seen that, in any case, the conductor is
only the core of a disturbance which extends to great distances on all
sides. Were the clouds, the earth and the streak of heated air called the
lightning flash all perfect conductors we could calculate the entire dis-
turbance. It might then consist of a series of stationary waves between
the two planes, extending indefinitely on all sides but with gradually de-
creasing amplitude as we pass away from the centre. The oscillations,
once set up, would go on forever, as there wo-uld be no poor conductors to
damp them. But when the clouds and the path of tihie hghtning both
have very great resistance, the energy is very soon converted into heat
and the oscillations destroyed. I have given it as my opinion that this
is generally the case and that the oscillations seldom take place, but I
may be wrong, as there is little to guide me except guesswork. If they
take place, however, we have a ready explanation of what is sometimes
called a back stroke of lightning. That is, a man at the other end of
the cloud a mile or more distant from the lightning stroke somotimos re-
ceives a shock, or a new lightning flash may form at that point and kill
him. This may be caused, according to our present theory, by the
arrival of the waves of electrical disturbance which might themselves
cause a slight shock or even overturn the equilibrium then existing and
cause a new electric discharge.

We have now considered the case of oscillations of electricity in a few
instances and can turn to that of steady currents. The closing of an
(doctrio current sends ethereal waves throughout space, hut after the
first shock the current flows steadily without producing any moro waves.
However, the properties of the space around the wire have been per-
manently altered, as we have already seen. Lot us now study these prop-
erties more in detail. I have before me a wire in which I can produce a
powerful current of electricity, and we have seen that the space around
it has been so altered that a delicately suspended magnetic needle can-
not remain quiet in all positions but stretches itself at right angles to

666

Hbney a. Rowlan'd

the wire, the north pole tending to reToWe around it in one direction
and the south pole in the O'ther. This is a very old experiment, but we
now regard it as evidence that the properties of the space around the wire
have been altered rather than that the wire acts on the magnet from a
distance.

Put, no-w, a plate of glass around the wire, the latter being vertical
and the former with its plane horizontal, and pass a powerful current
through the wire. On now sprinkling iron filings on the plate, they
arrange themselves in circles around the wire and thus point out to us
the celebrated lines of magnetic force of Faraday. Using two wires
with currents in the same direction we get these other curves, and, test-
ing the forces acting on the wire, we find that they are trying to move
towards each other.

Again, pass the currents in the opposite directions and we get these
other curves and the currents repel each other. If we assume that the
lines of force are like rubber bands, which tend to shorten in the direc-
tion of their length and repel each other sideways, Faraday and Maxwell
have showm that all magnetic attraction and repulsions are explained.
The property which the presence of the electric current has conferred on
the luminiferous ether is then one by which it tends to shorten in one
direction and spread out iu the other two directions.

We have thus done away with action at a distance, and have account-
ed for magnetic attractio'n by a change in the intervening medium as
Faraday partly did almost fifty years ago. For this change in the sur-
rounding medium is as much a part of the electric current as auy thing
that goes on within the wire.

To illustrate this tension along the lines O'f force, I have constructed
this model, which represents the section of a coil of wire with a bar of
iron within it. The rubber bands represent the lines of force which pass
around the coil and through the iron bar, as they have an easier passage
through the iron than the air. As we draw the bar down and let it go,
you see that it is drawn upward and oscillates around its position of
equilibrium until friction brings it to rest. Here, again, I have a coil
of wire with an iron bar within it with one end resting on the floor.
As we pass the current and the lines of magnetic force form around
the coil and pass through the iron, it is lifted upwards although if
weighs 24 pounds and oscillates around its position of equilibrium
exactly the same as though it were sustained by rubber bands as
in the model. The rubber bands in this ease are invisible to our
eye, but our mental vision pictures them to us as lines of magnetic

Modern" Views with Respect to Electric Currents 667

force iR the luminiferous ether drawing the bar upward by their con-
tractile force. This contractile force is no small quantity, as it may
amount, in some cases, to one or even two hundred pounds to the square
inch, and thus rivals the greatest pressure which we "use in our steam
engines.

Thus the luminiferous etlier is, to-day, a much more important factor
in science than the air we breathe. We are constantly surrounded by
the two, and the presence of the air is manifest to us all; we feel it, he
hear by its aid, and we even see it, under favorable circumstances, and
the velocity of its motion as well as the amount of moisture it carries is a
constant topic of conversation with mankind at large. The luminifer-
ous ether, on the other hand, eludes all our senses and it is only witli
imagination, the eye of the mind, that its presence can be perceived.
By its aid in conveying the vibrations we call ligh"!^ we are enabled to see
the world around us, and by its other motions which cause magnetism,
the mariner steers his ship through the darkest night when the heavenly
bodies are hid from view. When we speak in a telephone, the vibra-
tions of the voice are carried forward to the distant point by waves in
"the luminiferous ether, there again to be resolved into the sound waves
of the air. When we use the electric light to illuminate our streets, it
is the luminiferous ether which conveys the energy along the wires as
well as transmits it to our eye after it has assumed the form of light.
We step upon an electric street car and feel it driven forward with tlie
power of many horses, and again it is the luminiferous ether, whose im-
mense force we have brought under our control and made to serve our
purpose. ITo longer a feeble, uncertain sort of medium, but a mighty
power, extending throughout all space and binding the whole universe
together, so that it becomes a living unit in which no one portion can ho
changed without ultimately involving every other portion.

To this, ladies and gentlemen, we have been led hy the study of elec-
trical phenomena, and the ideas which I have set forth constitute the
most modern views held by physicists with respect to electric currents.

THE HIGHEST AIM OE THE PETTSICIST

A.D])KB8B BBLIVBBBD AS PRESIDENT OP THE AMBRIOAN PHYSIOAIi BOOIBTT, AT ITS
MEETING IN NEW TOBK, OOTOBEB 38, 1899

{Armrican Journal of Science [4] VIII, 401-411, 1899; Science, X, 836-888, 1899;;
lohna Eophim Vhivereity Oirculare, No. 148, pp. 17-30, 19001

Q-bntlbmbn and Fellow Phtsioibts oe Ambgemoa: — ^We meet to-day
OD an occasion which, marks an epoch, in the history of physics in Amer-
ica; niay the future show that it also marks an epoch in the history of
the science which this society is organized to cultivate I For we meet
here in the interest of a science above all sciences which deals with the
fonndation of the universe, with the constitution of matter from- which
everything in the universe is made and with the ether of space by which
alone the various portions of matter forming the universe affect each
other even at such distances as we may never expect to* traverse, what-
ever the progress of onr science in the future.

We, who have devoted our lives to the solution of problems connected
with physics, now meet together to help each other and to forward the
interests of the subject which we love, — a subject which appeals most
strongly to the better instincts of our nature and the problems which
tax our minds to the limit of their capacity and suggest the grandest
and noblest ideas of which they are capable.

In a country where the doctrine of the equal rights of ma.-n has been
distorted to mean the equality of man in other respects, we form a small
and unique body of men, a new variety of the human race, as one of
our greatest scientists calls it, whose views of what constitutes the gi'eat-
est achievement in life are very different from those around us. In this
respect we form an aristocracy, not of wealth, not of pedigree, but of
intellect and of ideals, holding him in the highest respect who adds the
most to our knowledge or who strives after it as the highest good.

Thus we meet together for mutual sympathy and the interchange of
knowledge, and may we do so ever with appreciation of the benefits to
ourselves and possibly to our science. Above all, let us cultivate the
idea of the dignity of our pursuit so that this feeling may sustain us in
the midst of a world which gives its highest praise, not to the investiga-

The Highest Aim of the Physicist

669

tion in the pure ethereal physics vhich our society is formed to cultivate,
but to the one who- uses it for satisfying the physical rather than the
intellectual needs of mankind. He who makes two blades of grass grow
where one grew before is the benefactor of mankind; but he who ob-
scurely worked to find the laws of such growth is the intellectual supe-
rior as well as the greater benefactor of the two.

How stands our country, then, in this respect? My answer must still
be now, as it was fifteen years ago, that much of the intellect of the
country is still wasted in the pursuit of so-called practical science which
ministers to our physical needs and but little thought and money is
given to the grander portion of the subject which appeals to our intellect
alone. But your presence here gives evidence that such a condition is
not to last forever.

Even in the past we have a few names whom scientists throughout the
world delight to honor: Franklin, who almost revolutionized the
science of electricity by a few simple hut profound experiments; Count
Eumford, whose experiments almost demonstrated the nature of heat;
Henry, who might have done much for the progress of physics had he
published more fully the results of his investigations; Mayer, whose
simple and ingenious experiments have been a source of pleasure and
profit to many. This is the meager list of those whom death allows me
to speak of and who have earned mention here by doing something for
the progress of our science. And yet the record has been searched for
more than a hundred years. How different had I started to record
those who have made useful and beneficial inventions!

But I know, when I look in the faces of those before me, where the
eager intellect and high purpose sit enthroned on bodies possessing the
vigor and strength of youth, that the writer of a hundred years hence
can no longer throw such a reproach upon our country. Nor can we
blame those who have gone before us. The progress of every science
shows us the condition of its growth. Very few persons, if isolated in
a semi-civilized land, have cither the desire or the opportunity of pur-
suing the higher branches of science. Even if they should be able to do
so, their influence on their science depends upon what they publish
and make known to the world. A hermit philosopher we can imagine
might make many useful discoveries. Yet, if he keeps them to himself,
he can never claim to have benefited the world in any degree. His un-
published results are his private gain, but the world is no better off
until he has made them known in language strong enongh to call atten-
tion to them and to convince the world of their truth. Thus, to encour-
age the growth of any science, the host thing we can do is to meet

670

Henkt a. Eowland

together in its interest, to discuss its prohlems, to criticise each other^s
work and, best of all, to provide means by which the better portion of
it may be made known to the world. Furtlieimore, let us encourage
discrimination in our thoughts and work. Let us recognize the eras
when great thoughts have been introduced into our subject and let uis
honor the great men who introduced and proved them correct. Let us
forever reject such foolish ideas as the equality of mankind and care-
fully give the greater credit to the greater man. So, in choosing the
subjects for our investigation, let us, if possible, work upon those sub-
jects which will finally give us an advanced knowledge of some great
subject. I am aware that we cannot always do this: our ideas will often
fiow in side channels: but, with the great problems of the imiverse
before us, we may some time be able to do our share toward the greater
end.

What is matter; what is gravitatio-n; what is ether and the radiation
through it; what is electricity and magnetism; how are these connected
together and what is their relation to- heat? These are the greater
problems of the universe. But many infinitely smaller problems we
must attack and solve before we can even guess at the solution of the
greater ones.

In our attitude toward these greater problems how do we stand and
what is the foundation of our knowledge?

Newton and the great array of astronomers who have succeeded him
have proved that, within planetary distances, matter attracts all others
with a force varying inversely as the square of tlie distance. But what
sort of proof have we of this law? It is derived from astronomical
ohservations on the planetary orbits. It agrees very well within these
immense spaces; but where is the evidence that tlic law holds for smaller
distances? We measure the lunar distance and the size of the earth,
and compare the force at that distance with the force of gravitation on
the earth^s surface. But to- do this we must com])are the matter in the
earth with that in the sun. This wo can only do by a-smmmg the law
to be proved. Again, in descending from the earth’s gravitation to that
of two small bodies, as in the Cavendish experiment, wo assume the law
to hold and deduce the mass of the earth in terms of our unit of mass.
Hence, when we say that the mass of the earth is times that of an
equal volume of water we assume the law of gravitation to be that of
Newton. Thus a proof of the law from planetary down to terrestrial
distances is physically impossible.

Again, that portion of the law which says that gravitational attrac-

The Highest Aim of the Physicist

671

tion is proportional to the quantity o-f matter, wliicli is tie same as
saying that the attraction of one body by another is not aflEected by the
presence of a third, the feeble proof that *we give by w^eighing bodies in
a balance in different positions with respect to each cannot be accepted
oh a larger scale. When we can tear the sun into two portions and prove
that either of the two halves attracts half as much as the whole, then
we shall have a proof worth mentioning.

Then as to the relation of gravitation and time what can we say?
Can we for a moment, suppose that two bodies moving through space
with great velocities have their gravitation unaltered? I think not
ITeither can we accept Laplace^s proof that the fo-ree of gravitation acts
instantaneously through space, for we can readily imagine some com-
pensating features unthought of by Laplace.

How little we know then of this law which has been under observa-
tion for two hundred years!

Then as to matter itself how have our views changed and how are
they constantly changing. The round hard atom of Newton which
Q-od alone could break into pieces has become a molecule composed of
■many atoms, and each of these smaller atoms has become so elastic that
after vibrating 100,000 times its amplitude of vibration is scarcely
diminished. It has become so complicated that it can vibrate with as
many thousand notes. We cover the atom with patches of electricity
here and there and make of it a system compared with which tlie plane-
tary system, nay the luiiverse itself, is simplicity. Nay more: some of
UR even claim the power, which Newton attributed to God alone, of
hreaking the atom into smaller pieces whose size is left to the imagina-
tion. "Vniere, then, is that person who ignorantly sneers at the study
of matter as a material a*nd gross study? Where, again, is that man with
gifts so God-like and mind so elevated that he can attack and solve its
problem?

To all matter we attribute two properties, gravitation and inertia..
Without these two matter cannot exist. The greatest of the natural
laws states that the power of gravitational attraction is proportional to
the mass of the body. This law of Newton, almost neglected in the
thoughts of physicists, undoubtedly has vast import of the very deepest
meaning. Shall it mean that all matter is finally constructed of uniform
and similar primordial atoms or can we find some other explanation?

That the molecules of matter are not round, we know from the facts
of crystallography and the action of matter in -rotating the plane of
polarization of light.

672

Henbt a. Eowland

Tha.t portions of the mo-lecnles and even of the atoms are electrically
charged, we knovr from electrolysis^ th^ action of gases in a vacuum
tube and from the Zeeman effect.

That some of them act like little magnets, we know from the mag-
netic action of iron, nickel and cobalt.

That they are elastic, the spectrum shows, and that the vibrating
portion carries the electrified charge with it is shown by the Zeeman
effect

Here, then, we have made quite a start in our problem: but how far
are we from the complete solution? How can we imagine the material
of which ordi n a r y or primordial atoms are made, dealing as we do only
with aggregation of atoms alone? Forever beyond our sight, vibrating
an almost infinite number of times in a second, moving hither and yon
with restless energy at all temperatures beyond the absolute zero o-f
temperature, it is certainly a wonderful feat of human reason and
imagination that we know as much as we do at present. Encouraged by
these results, let us not linger too long in their contemplation but press
forward to the new discoveries which await ns in the future.

Theu as to electricity, the subtile spirit of the amber, the demon who
reached out his glutinous arms to draw in the light bodies within his
reach, the fluid which could run through metals with the greatest ease
hut could he stopped by a fruil piece of glass! Where is it now? Tan-
ished, thrown on the waste heap of our discarded theories to be replaced
by a far nobler and exalted one of action in the ether of space.

And so we are brought to consider that other great entity — ^the ether:
filling all space without limit, we ima.gine the ether to be the only
means by which two portions of matter distant from each other can
have any mutual action. By its means we imagine every atom in the
universe to be bound to every other atom by the force of gravitation
and often by the force of magnetic and electric action, and we conceive
that it alone conveys the vibratory motion of each atom or molecule
out into space to be ever lost in endless radiation, passing out into
infinite space or absorbed by some other atoms which happen to be in
its path. By it all electromagnetic energy is conveyed from the feeble
attraction of the rubbed amber through the many thousand horse-power
conveyed hy the electric wires from Niagara to the mighty rush of
energy always flowing from the sun in a flood of radiation. Actions
feeble and aetioLB mighty from inter-molecular distances through inter-
planetary and inter-stellar distances until we reach the mighty dis-
tances which bound the universe — all have their being in this wondrous
ether.

The Hkjhesx Aim of the Physioibt

673

And yet, however wonderful it may be, its laws are far more simple
than, those of matter. Every wave in it, whatever its length or inten-
proceeds onwards in it according to well known laws, all with the
same speed, unaltered in direction from its source in electrided matter,
to the confines of the univei’se unimpaired in eiiorgy unless it is dis-
turbed by the presence of matter. However the waVes may cross each '
other, each proceeds by itself without interference with the others.

So with regard to gravitation, we have no evidence that the presence
of a third body aSects the mutual attraction of two other bodies or
that the presence of a third quantity of electricity affects the mutual
attraction of two other quantities. The same for magnetism.

Eor this reason the laws of gravitatio'n and of electric and magnetic
action including radiation are the simplest of all laws when we condSne
them to a so-called vacuum, but beco'me more and more complicated
when we treat of them in space containing matter.

Subject the ether to immense deotrostatic, magnetic or gravitational
forces and wc find absolutely no signs of its breaking down or even
change of properties. Set it into vibration by means of an intensely
hot body like that of the sunnnd it conveys many thousand horse-power
for each square foot of surface as quietly and with apparently unchanged
laws as if it were conveying the energy of a tallow dip.

Again, subject a millimeter of ether to the stress of many thousand,
nay even a million, volts and yet we see no signs of breaking down.

Hence the properties of the ether are of ideal simplicity and lead to
the simplest of natural laws. All forces which act at a distance, always
obey the law of the inverse square of the distance and we have also the
attraction of any number of parts placed near each other equal to the
arithmetical sum of the attractions when those parts are separated. So
also the aimplo law of ethoreal wavos which has inentiontul above.

At the present time, through the labors of Maxwell supplemented by
those of Hertz and others, we have arrived at the great generalization
that all wave disturbances in the ether are electromagnetic in their
nature. Wc know of little or no cthcroiil (liHl,nrban<t(^ which can bo sot
up by tlie inotaon of matter alone: the matter must he cloetrifiod in
order to have sufficient hold on tho etlier to communicate its motion
to the ether. Tho Zeeman ofloct even shows this to be the case where
molecules arc concerned and when the jnsriod of vibra.tion is immensely
great. Indeed the experiment on the magnetic action of electric con-
vection shows tho same thing. By electrifying a disc in motion it
appears as if tho disc holds fast to the other and drags it with it, thus
setting tlio jKiculiar ctiicrcal motion known as inagiiotism.

674

Hbnbt a. Eowiand

Have we not another case of a similar nature when a huge gravitar
tional mass like that of the earth revolves on its axis? TTafi not matter
a feeble hold on the ether sufficient to produce the earth’s magnetism?

But the e^eriment of Lodge to detect such an action apparently
showed that it must be very feeble. Might not his experiment have
succeeded had he used an electrified revolving disc?

To detect something dependent on the relative motion of the ether
and matter has been and is the great desire of physicists. But we
always find that, with one possible exception, there is always some com-
pensating feature which renders our efforts useless. This one experi-
ment is the aberration of light, but even here Stokes haa shown that it
may be explained in either of two ways: first, that the earth moves
through the ether of space without disturbing it, and second, that it
carries the ether with it by a kind of motion called irrotational. Even
hefe, however, the amount of action probably depends upon relative
motion of the luminous source to the recipient telescope.

So the principle of Doppler depends also on this relative motion and
IS independent of the ether.

The result of the experiments of Foucault on the passage of light
through moving water can no longer be interpreted as due to the partial
movement of the ether with the moving water, an inference due to
imperfect theory alone. The experiment of Lodge, who attempted to
set the ether in motion by a rapidly rotating disc, showed no such result.

The experiment of Miehelson to detect the ethereal wind, although
earned to the extreme of accuracy, also failed to detect any relative
motion of the matter and the ether.

But matter with an electrical charge holds fast to the ether and
moves it in the manner required for magnetic action.

When electrified bodies move together through space or with refer-
ence to each other we can only follow thtir mutual actions through very
slow and uniform velocities. When they move with velocities com-
parable with that of light, equal to it or even beyond it, we calculate
their mutual actions or action on the ether only by the light of our
imagination unguided by experiment. The conclusions of J. J. Thom-
son, Seaviside and Hertz are all results of the imagination and they all
rest upon assumptions more or less reasonable but always assumptions.
A ixiathematical investigation always obeys the law of the conservation
of knowledge: we never get out more from it than we put in. The
knowledge may be changed in form, it may be clearer and more exactly
stated, but the total amount of the knowledge of nature given out by

The Highest Aim of the Physicist

675

the investigation is the same as we started with. Hence we can never
predict the result in the case of velocities beyond our reach, and such
calculations as the velocity of the cathode rays from their electro-
magnetic action has a great element of uncertainty which we should do
well to remember.

Indeed, when it comes to exact knowledge, the limits are far more
circumscribed.

How is it, then, that we hear physicists and others constantly stating
what will happen beyond these limits? Take velocities^ for instance,
such as that of a material body moving with the velocity of light. There
is no known process by which such a velocity can be obtained even
though the body fell from an infinite distance upon the largest aggrega-
tion of matter in the universe. If we electrify it, as in the cathode
rays, its properties are so changed that the matter properties are com-
pletely masked by the electromagnetic.

It is a common error which young physicists are apt to fall into to
obtain a law, a curve or a mathematical ecucpression for given experi-
mental limits and then to apply it to points outside those limits. This
is sometimes called extrapolation. Such a process, unless carefully
guarded, ceases to be a reasoning process and becomes one of pure
imagination specially liable to error when the distance is too great.

But it is not my purpose to enter into detail. What I have given
suffices to show how little we know of the profounder questions involved
in our subject.

It is a curious fact thai^ having minds tending to the infinite, with
imaginations unlimited by time and space, the limits of our exact
knowledge are very small indeed. In time we are limited by a few
hundred or possibly thousand years: indeed the limit in our science is
far less than the smaller of these periods. In space we have exact
knowledge limited to portions of our earth^s surface and a mile or so
below the surface, together with what little we can learn from loolring
through powerful telescopes into the space beyond. In temperature
our knowledge extends from near the absolute zero to that of the sun
but exact knowledge is far more limited. In pressures we go from the
Crookes vacuum still containing myriads of flying atoms to pressures
limited by the strength of steel but still very minute compared with the
pressures at the centre of the earth and sun, where the hardest steel
would flow like the most limpid water. In velocities w© are limited to
a few miles per second; in forces, to possibly 100 tons to the square
inch; in mechanical rotations, to a few hundred times per second.

676

Hbnky a. Rowland

All the facts which we have considered, the liability to error in what-
ever direction we go, the infirmity of our minds in their reasoning
power, the fallibility of witnesses and experimenters, lead the scientist
to be specially skeptical with reference to any statement made to him
or any so-called knowledge which may be brought to his attention. The
facts and theories of our science are so much more certain than those of
history, of the testimony of ordinary people on which the facts of
ordinary history or of legal evidence rest, or of the value of medicines to
which we trust when we are ill, indeed to the whole fabric of sxipposod
truth by which an ordinary person guides his belief and the actions of
his life, that it may seem ominous and strange if what I have said of
the imperfections of the knowledge of physics is correct. How shall we
regulate our minds with respect to it: there is only one way that I
know of and that is to avoid the discontinuity of the ordinary, indeed
the so-called cultivated legal mind. There is no such thing as absolute
truth and absolute falsehood. The scientific mind should never recog-
nize the perfect truth or the perfect falsehood of any supposed theory
or observation. It should carefully weigh the chances of tnxth and
error and grade each in its proper position along the line joining abso-
lute truth and absolute error.

The ordinary crude mind has only two compartments, one for truth
and one for error; indeed the contents of the two compartments are
sadly mixed in most cases: the ideal scientific mind, however, has an
infinite number. Each theory or law is in its proper compartment indi-
cating the probability of its truth. As a new fact arrives the scientist
changes it from one compartment to another so as, if possible, to always
keep it in its proper relation to truth and error. Thus the fluid nature
of electricity was once in a compartment near the truth. Faraday ^s and
Maxwell^s researches have now caused us to move it to a comimrtmont
nearly up to that of absolute error.

So the law of gravitation within planetary distances is far toward
absolute truth, but may still need amending before it is advanced farther
in that direction.

The ideal scientific mind, therefore, must always be held in a state
of balance which the slightest new evidence may change in one direction
or another. It is in a constant state of skepticism, knowing full well
that nothing is certain. It is above all an agnostic with respect to all
facts and theories of science as well as to all other so-called beliefs and
theories.

Yet it would be folly to reason from this that we need not guide our

The Highest Aim oe the Physioist

677

life according to the approach to knowledge that we possess. Nature is
inexorable; it punishes the child who unknowingly steps ofl a precipice
quite as severely as the grown scientist whO' steps over, with full knowl-
edge of all the laws of falling bodies and the chances of their being
correct. Both fall to the bottom and in their fall obey the gravitational
laws of inorganic matter, slightly modified by the muscular contortions
of the falling object but not in any degree changed by the previous
belief of the person. Natural laws there probably are, rigid and un-
changing ones at that. Understand them and they are beneficent: we
can use them for our purposes and make them the slaves of our desires.
Misunderstand them and they are monsters who may grind us to powder
or crush us in tlie dust. Nothing is asked of us as to our belief: they
act xmswervingly and we must understand them or suffer the conse-
quences. Our only course, then, is to act according to the chances of
our knowing the right laws. If we act correctly, right; if we act incor-
rectly, we suffer. If we are ignorant we die. What greater fool, then,
than he who states that belief is of no consequence provided it is sincere.

An only child, a beloved wife, lies on a bed of illness. The physician
says that the disease is mortal; a minute plant called a iniorolw has
obtained entrance into the body and is growing at the expense of its
tissues, foiTuing deadly poisons in the blood or destroying some vital
organ. The physician looks on withoxxt being able to do anything.
Daily he comes and notes the failing strength of his patient and daily
the patient goes downward until he rests in his grave. But why has the
physician allowed this? Can wo doubt that there is a remedy which
shall kill the microbe or neutralize its poison? Why, then, has he not
used it? Ho is employed to cure but has failed. Ilis bill wo cliccirfully
]ja.y because he has done his best and given a chance of euro, 'irho
answer is ignorance. The rcnmdy is yet unknown. The physiciiui is
waiting for others to discover it or perhaps is experimenting in a crude
and unscientific manner to find it. Is not the inference correct, then,
that the world has been paying the wrong class of men? Would not
this ignorance have been dispelled had the proper money been used in
the past to dis])el it? Such deaths some pcmplo consider an act of God.
What blasphemy to attribute to God that which is due to our own and
our ancestors’ selfishness in not founding institutions for medical re-
search in sufficient number and with sufficient means to discover the
truth. Such deaths are murder. Thus the present generation suffers
for tho sins of the past and wo die because our ancestors dissipated their
wealth in armies and navies, in the foolish pomp and eireumstance of

678

Hhnbt a. Eowlastd

society, aod neglected to provide us with a knowledge of natural laws
In this sense they were the murderers and robbers of future generations
of unborn millions and have made the world a charnel ho-use and place
of mourning where peace and happiness might have been. Only their
ignorance of what they were doing can be their excuse, but this excuse
puts them in the class of boors and savages who act according to selfish
desire and not to reason and to the calls of duty. Let the present gener-
ation ^e warning that this reproach be not cast on it, for it cannot
plead ignorance in this respect.

This illustration from the department of niedicine I have given be-
cause it appeals to all But all the sciences are linked together and
must advance in concert. The human body is a chemical and physical
problem, and these sciences most advance before we can conquer disease.

But the true lover of physics needs no such spur to his actions. The
cure of disease is a very important object and nothing can be nobler than
a life devoted to its cure.

The aims of the physicist, however, are in part purely intellectual:
he strives to understand the universe on account of the intellectiml
pleasure derived from the pursuit, but he is upheld in it by the knowl-
edge that the study of nature’s secrets is the ordained method by which
the greatest good and happiness shall finally come to the human race.

Where, then, are the great laboratories of research in this city, in
this country, nay, in the world?’ We see a few miserable structures here
and there occupied by a few starving professors who are nobly striving
to do the best with ihe feeble means at their disposal. But where iii
the world is the institute of pure research in any department of science
with an income of $100,000,000 per year? Wliere can the discorcror in
pure science earn more than the wages of a day laborer or cook? But
$100,000,000 per year is but the price of an army or of a navy designed
to kill other people. Just think of it, that one per cent of this sum
seems to most people too great to save our children and descendants
from misery and even death!

But the twentieth century is near— may we not hope for better things

before its end? May we not hope to influence the public in this
direction?

Let us go forward, then, with confidence in the dignity of our pur-
suit. Let us hold our heads high with a pure conscience while we seek
the truth, ^d may the American Physical Society do its share now and
in generations yet to come in trying to unravel the great problem of
the constitution and laws of the universe.

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682

Hbnbt a. BowLAinD

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684

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Bibliogeapht

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56. The Arc-Spectra of the Elements. I. Boron and Beryllium. II.

Germanium. III. Platinum and Osmium. IV. Ehodium, Eu-
theiiium and Palladium. By H. A. Eowland and E. E. Tatuall.
Astrophysical Journal, I, 14-17, 149-163, 3896; 11, 184-187, 1896; III,
286-291, 1896.

57. Notes of Observations on the Eontgen Eays. By U. A. Rowland,

N. E. Carmichael and L. J. Briggs.

American Journal of Science (4), I, 247, 248, 180G.

Philosophical Magazine (6), XLl, 383-382, 1890.

58. Notes on Eontgen Eays. By H. A. Eowland, N. E. Carmichael and

L. J. Briggs.

Electrical World, XXVII, 452, 1896.

59. The Eontgen Eay and its Eelation to Physics.

Transactions of the American Institute of Electorical Engineers,
XIII, 403-410, 430, 431, 1896.

60. Electrical Measurement by Alteniating Currents.

American Journal of Science (4), IV, 429-448, 3897.

Philosophical Magazine (5), XLV, 06-86, 1898.

61. Arc— Spectra of Vanadium, Zirconium and Lanthanum. By H. A.

Eowland and C. N. Harrison.

Astrophysical Journal, VII, 273-294, 373-389, 1898.

686

Henry A. Eowland

62. Electrical Measurements. By H. A. Eowland and T. D. Penniman.

American Journal of Science (4), Vin, 36-67, 1899.

Johns Hopkins University Circulars No. 136, pp. 51, 63, 1898
(abstract) .

63. Eesistance to Ethereal Motion. By H. A. Eowland, H. E. Gilbert

and P. 0. McJimcMn.

Johns Hopkins University Circulars No. 146, p. 60, 1900.

64. Diffraction Gratings.

Encyclopaedia Britannica, New Volumes, in, 468, 459, 1903.

ADDEESSES

1. A Plea for Pure Science. Address as Vice-President of Section B
of the American Association for the Advancement of Science,
Minneapolis, August 15, 1883.

Proceedings of the American Association for the Advancement of
Science, XXXn, 105-136, 1883.

Science, n, 343-360, 1883.

Journal of the Franklin Institute, CXVI, 379-399, 1883.

2. The Physical Laboratory in Modem Education. Address for Com-

memoration Day of the Johns Hopkins University, February
22, 1886.

Johns Hopkins University Circulars No. 50, pp. 103-105, 1886.

3. Address as President of the Electrical Conference at Philadelphia,

September 8, 1884.

Report of the Electrical Conference at Philadelphia in September,
1884, Washington, 1886.

4. The Electrical and Magnetic Discoveries of Faraday. Address at

the Opening of the Electrical Club House of NTew York City,
1888.

Electrical Review, Peb. 4, 1888.

6. On Modem Vieire with Eespect to Electric Onrrents. Address
before the Americsn Institute of Electrical Engineers, New
York, May 82, 1889.

Traneactioiis of the American Institute of Mectrical Engineers, VI.
342-357, 1889.

Electrical World, Xm, p. 319, 1889.

See also Electrical World, XTTT, p. 142, i889.

Bibliography

687

6. The Highest Aim of the Physicist. Address as President of the
American Physical Society, Hew York, October 28, 1899.

Science, X, 825-833, 1899.

American Journal of Science (4), VIII, 401-411, 1899.

Johns Hopkins University Circnlars No. 148, pp. 17-20, 1900.

EEPOETS AHD BOOKS

1. Eeport of the Electrical Commission Appointed to Consider the

Location, Arrangement and Operation of Electric Wires in the
District of Columbia, Washington, 1898.

By Andrew Rosewater, H. A. Rowland, and Francis B. Skunk.

2. Elements of Physics.

By H. A. Rowland and J. S. Ames, New yorlc, 1900, XIII -|- 268. pp.

DESCRIPTION

DIVIDING ENGINES

A DESCEIPTIOlSr OF THE DIVIDING ENGINES DESIGNED
BY PBOPESSOE EOWLAND/

Three dividing engines were made under Professor Eowland^s direc-
tion, all embodying the same general principles as given in his article
on the Screw in the Encyclopedia Britannica (this volnme p. 606).
The screws of all three have approximately twenty threads to the inch;
and the number of teeth in the ratchet wheels of the first, second and
third machines is such that they rtile 14,438, 16,020 and 20,000 lines in
an inch. The three machines are kept in the snb-basement of the
Physical Laboratory of the Johns Hopkins University under such con-
ditions as will secure a piuctically constant temperature for long
intervals of time. Each machine is driven by a separate water-motor
whose speed can be regulated at will.

The machines have been used almost exclusively for the ruling of
dififraction gratings, although a few centimetre scales have been made.
The gratings have been, with only four or five exceptions, made of
" speculum metal," having the composition, copper 126 lbs. 4 oz., tin
68 lbs. 9 oz., and as homogeneous as possible. The rough metal plates
were cast under Professor Eowland^s direction, and were then figured
and polished. After the ruling was completed, the gratings were care-
fully tested in order to see if they were free from ghosts," diflPused
light and defective definition.

To test the screw, ratchet-hcad and thrust screw for periodic errors.
Professor Eowland used the following method: he ruled a space of
about one centimetre on a polished surface, then pushed the carriage
back this distance, turned the grating-holder through a minute angle
and again ruled a surface of about the same width as before. There is
thus produced a cross-ruling, the lines being slightly inclined to each
other; and when examined by reflected light, a series of undulations is

1 Unfortunately Professor Rowland never published a description of these machines ;
and the Committee has failed to And any Information concerning the inception of
the idea or the history of the construction of the first machine. It has been
thought best, therefore, to give, first, a general description of the design of the
engines with various necessary details of some of the working parts and, second,
drawings made to scale, showing all the connections of the intricate mechanism;
both of these have been prepared under the 'direction of J. S. Ames, Secretary of
the Committee, and have been approved by the Committee.

692

Hbmtbt a. Bowlaot

seen to cross the lines at right angles, corresponding to the points of
intersection of the two sets of rulings. This pattern resembles closely
in appearance that of watered, silk. The corrector of the machine is
adjusted until this undulatory pattern is as regular and. has as small
an amplitude as possible.

Any description of Eowland^s dividing engines, however brief, would
be incomplete without some mention of Mr. Theodore Schneider who
for twenty-five years was Professor Eowland^s mechanician and assistant
and who died only a few weeks before him. It was he who made the
screws and most of the working parts of the machines, and it was he
who superintended the ruling of every grating that has left the Physical
Laboratory of the Johns Hopkins TJniversity for use elsewhere in the
world.

General Design of Dividing Engine*

The object of this machine is to rule straight lines on metal or glass
surfaces, exactly parallel and at exactly equal distances apart. The sur-
face to be ruled is attached to a frame which is moved forward by a nut
as it is advanced by a screw; the ruling edge is generally a diamond
mounted in such a manner as to be drawn to and fro across the surface to
be ruled, but to be in contact with it during only one of these motions.

Eotaxy motion is imparted to the main shaft (48 A) by means of a
driving pulley, operated by a belt attached to a water motor (not shown
in the cuts). Mounted on the main shaft are the cams (46, 47) for
operating the pawl-levers, which turn the screw and advance the nut;
the cam (56) controlling the mechanism for raising the diamond; and
the crank (50) which by means of the connecting rod and cross-head
impart a reciprocating motion to the ruling carriage and its diamond.
By means of adjustments in the crank and connecting rod, the length
of stroke of the diamond may be varied, and rulings of different lengths
are thus obtained.

In each revolution of the main shaft, the cycle of operations that occur
is as follows: Let the diamond be on the plate in a position to begin
ruling. It is moved forward, i. e. toward the shaft, by means of the
ruling frame and parts described, and a line is ruled. The stroke of
the engine being now about to reverse, the cam controlling the mechan-
ism for lifting the diamond performs its duty; and, while the engine
is on its return stroke, with the diamond off the plate, the latter is

s The figures In the text refer to the numbered parts in the cuts which follow the
article.

Dbsobiption op the Dividing Engines

693

advanced a space equal to the desired distance between the rulings.
This is done by the cams operating the pawl-levers (26 and 40), which
cause the pawl (41) to rise to a pre-determined position corresponding
to one or more teeth of the graduated ratchet head, then to engage this
wheel and, being now forced down to its normal position, to cause the
wheel and the feed-screw, to which it is attached, to turn through a
small definite angle. The rotation of the screw causes the nut to
advance towards the ratchet head; and the nut pushes forward the
plate-carriage to which the plate to be ruled is secured. The engine
being now at the end of its return stroke, the diamond is lowered into
contact with the plate, and is ready for ruling the next line. These
operations are repeated until the requisite number of lines is ruled.
During each cycle of operations a slight additional motion is imparted
to the nut and thus to the plate-carriage by means of the corrector
mechanism, in order that any periodic errors of the screw, screw-head,
etc., may be eliminated.

The ruling-carriage with its diamond holder moves along truncated
V-ways, as shown in the cuts, the surfaces in contact being the
steel ways and the box-wood linings to the grooves on the carriage.
These box-wood linings press against both the sides and the top of the
ways and are adjustable. The plate-carriage moves along V-ways, the
surfaces in contact being the steel ways and the cast-iron carriage.
These two pairs of ways are accurately at right angles to each other.

Detailed Desoriptionr

I. Mechanism connecting the plate-ca.rriage and the nut. Sec Pig. 5.

The plate-carriage carries a thrust collar (20) through which the

feed-screw passes freely. It is held in position by pins engaging in the
top and bottom of the platc-carriage. The thrnst of the nnt in advan-
cing is commimicatod by two Ings, one on each side of the nnt casings
(21), to two correspondingly located screw-heads in the thrust collar;
and, finally, screw-heads in the top and bottom of the thrnst-collar
transfer the thmst to correspondingly located lugs (22) in the jfiato-
carriag(‘.

II. Pawl mechanism. See Pig. 4.

The degree of rotation imparted to the graduated ratchet-head de-
pends upon the number of teeth the pawl engages in each revolution
of the main-shaft and may be varied by altering the size of the cams
(46 and 47) on which the pawl-levers 26 and 40 rest. The pawl-lever

(594

Henry A. Rowland

(26), to which the hell-crank (42) is pivoted, causes the pawl to rise to a
height corresponding to the number of teeth to be engaged on the
graduated ratchet-head. The other lever (40) has the function of
engaging and disengaging the pawl. The cycle of operations that
occurs in one revolution of the main shaft is as follows: The pawl-lever
(26) is raised by the cam (47), and in so doing gauges the degree of
revolution to be imparted to the graduated ratchet-head and feed-
screw. The other lever (40), which is pivoted on the pawl-lever (26),
is raised further, and thereby permits cam (46) and the beU-erank (42)
to carry the pawl (41) forward into engagement with the graduated
ratchet-head. The weight (45) attached to the bell-crank arm insures
a positive engagement of the pawl. The depth to which the pawl enters
between the teeth of the graduated ratchet-head is governed by the
adjusting screw (43) and a stop on pawl-lever (26). The pawl being
engaged, both levers (26 and 40) now descend, causing the graduated
ratchet-head and feed-screw to turn to an extent governed by the
number of teeth engaged. Lever (40) now descends to a position coin-
cident with that of the lever (26), and in so doing causes the stop on
lever (40) to press against the adjusting screw (44) on the bell-crank,
and thereby withdraws the pawl from the teeth of the graduated ratchet-
head.

III. Diamond and ruling head. See Pigs. 1 and 5.

The diamond (1) is firmly secured by means of solder in a holder
(2), which may adjusted to different inclinations. The frame
carrying the diamond, holder and dash-pot has an axle, centering in
bearing screws (3) and contained in an adjustable support (4). This
support may be raised or lowered to meet the requirements of plates of
different thickness. Normally, the end of the frame carrying the
diamond and holder, owing to its predominance of weight, would cause
the diamond to be in contact with the plate continuously. In order to
raise it on the return stroke of the engine, a weighted lift rod (57) is
caused to press on the end of the frame near the dash-pot. The height
to which the diamond is thus lifted off the plate is governed by nuts,
which may be adjusted on the stem of the lift-rod and which on their
descent come to rest on the plate 56 A.

The raising of the weighted lift-rod is primarily caused by cam (55)
on the main shaft; the inteimediate mechanism consists of the lever
(54), vertical oscillating rod (53), reciprocating rod (35), rocking stem
(34), and lifting lever (56). The action of the dashers and dash-pot

Dbsoeiption op the Dividing Engines

695

filled witli oil is to dampen any vibrations of the frame which carries
the diamond, and to check its descent o-n the plate.

IV. Corrector mechanism. See Pigs. 1, 4 and 5.

The wear of the threads contained in the lignum vitas plugs of the
split nutrcasing is taken up by the screws in the adjusting rings (17),
bringing the two parts of the nut closer to the feednscrew. Each side
of the nut is provided with a wing-shaped lever, the lower ends o-f which
are confined in guides forming part of the lower corrector frame (89);
but they are free to travel in the direction that the nut moves. T!^en
the screw is turning and the nut advancing, these wings are pressed
tight against the guide-plate (39 A) of the corrector frame; and thus
the nut will receive additional motions from any displacement of the
corrector. In this ihaiiner periodic errors of the screw may be neutral-
ized by the action of the corrector. The precise amount of correction
is controlled by the adjustments of the eccentric (25), This gives the
requisite amount of movement at the proper instants to the corrector
lever (28), which in turn moves the rocking shaft, corrector frame,
crank, lower frame and, finally, the wings of the nut. The disc (24)
may be adjusted and clamped, as shown in Pig. 4, in different positions
in the plane of the graduated ratchet-head; and the position of the
corrector eccentric (25) with respect to a fixed radius of the graduated
ratchet-head must be such as to make the phase of the correction oppo-
site that of the periodic error. The amount of eccentricity of the eccen-
tric can be varied by means of set-screws, as is evident from the cut;
and this must be regulated so that the amplitude of the correction
equals that of the periodic error.

Descriptive Drawings oe Dividing Engine No. 3

At the end of this article are five cuts of dividing engine No. 3, drawn
to scale, one quarter of the actual size, showing different views and
operations. They may be descrilxid as follows:

Pig. 1. Side elevation, showing the engine in a ruling position.

Pig. 2. Plan view of the foregoing.

Pig. 3. Plan view, showing the plate-carriage. The plate, plate-
holder and ruling-head are omitted.

Fig. 4. Side elevation opposite to Pig. 1, showing the engine in
the return stroke position.

Pig. 5. Transverse sectional elevation, showing the feed-screw, nut,
etc. The mechanism actuating the corrector-frame is shown as an
end-view.

696

Humt-Y A. Som>AND

BaplamMon of Numbers in the Outs
(Similax aumeials refer to like parts throughout the different Tiews.)

1. Buliug diamond.

2. Adjustable diamond holder.

3. Adjustable support for the axis of the diamond-frame.

4. Buling-head, carrying ruling mechanism.

5. Bods of the ruling carriage.

6. Plate to he ruled.

7. Adjustable box-wood elides of ruling carriage. (S’. B. — There are

box-wood slides pressed against the sides as well as the top of
the ways of the frame.)

8. Plate-holder.

9. Clamps for plate-holder.

10. Bed-plate.

11. Plate-carriage, which is moTed by the nut and which rests on ways.

(B". B. — The plate-carriage Ijas a cross-beam below the feed-
screw. See Pig. 5.)

18. Feed-screw.

13. Hardened steel step in end of feed-screw.

14. Hardened steel thrust-screw.

15. Casing of the split nut, holding the plugs 16.

16. Lignum Titse plugs, tapped for engaging feed-screw.

17. Adjusting rings for nut, with their adjusting screws.

18 and 19. Wings of the nut, controlled by the corrector, 39 A.

SO. Thrust collar, loosely attached to plate-carriage, 11.

81. Abutting lugs, rigidly attached to nut-casing 16, and in contact
with collar 30.

83. Abutting lugs of plate-carriage, in contact with screw-heads in
collar 30.

33. Graduated ratchet-head attached to the feed-screw.

34. Disc for phase-adjustment of corrector, being movable around the

axis of the screw in the plane of the ratchet wheel.

36. Eccmtric for adjusting amplitude of corrector, being movable
around an axis near one end so as to vary the eccentricity.

36. Pawl-lever, which raises or lowers the pawl, when it is disengaged

or engaged, respectively, in the ratchet wheel by means of lever
40.

37. Hollow arbor, serving as pivot for pawl-lever.

38. Corrector lever, resting on 85, and pivoted at 31.

39. Corrector frame.

Dssoeiption or the Diyidihg Engin-es

697

30. Hardened steel eenti’es for coinector frame.

31. Eoeldbig shaft, rotated hy means of lever 38.

32. Bearing for wrist-pin of lower correcto'r frame.

33. Crank for roeking correetorj a slight rotation of the shaft 31, thus

giving a slight sidewise motion to the frame 39.

34. EocMng stem, whidi moves the lifting-lever 66, of ruling head.

36. Eod to communicate reciprocating motion to 34.

36. Eaee-frame of engine.

37. Casings of ruling carriage, holding the adjustable bOx-wood slides, 7.

38. Adjustable weight for corrector lever.

39. Lower correetor frame, moved by the crank 33.

39 A. Corrector guide-plate, along which the wings of the nut move.

40. Lever for engaging and disengaging pawl, by means of bell-crank 42.

41. Pawl, driving ratchet wheel.

42. Bell-crank which is pivoted on 26; to one end the pawl is attached,

and the other is raised by the lever 40 and lowered by the
weight 46.

43 and 44. Adjusting screws attached to 42, for regulating the pawl
engagement. The stops are attached to 36 and 40.

45. Weight hanging from bell-crank.

46. Cam operating lever, 40; attached to main shaft.

47. Cam operating pawl-lever, 26; attached to main shaft.

(These two cams regulate the number of teeth of ratchet wheel
which the pawl clears each revolution of the main-shaft.)

48. Driving pulley, attached to main shaft.'

48 A. Main ^aft.

49. Connecting rod to give reciprocating motion to diamond-holder hy

means of 62 and 37.

50. Crank arm, designed to vary the length of stroke of the diamond.

51. Bar connecting cross-head 62, and ruling frame 37.

62. Cross-head, driven hy connecting rod 49.

63. Oscillating rod, connecting 35 and 64.

64. Lever operating stop mechanism for lifting diamond, resting on 65.

65. Cam attached to main shadft and operating the lever 64.

66. Lever for lifting rod 67; it is operated hy the rocking-stem 84.

66 A. Stop-plate regiilating drop of rod 87.

57. Eod for lifting diamond.

58. Daah-pot attached to the lever which carries the diamond-holder 2,

and which is pivoted at 3.

59. Adjustments for holding and regulating the dashers.

Fig. 1

Side elevation, showing the engine in a ruling position

Fig. 2

Plan view of the foregoing

Fig. )

I’lan view, showing the plate-carriage. The plate, plate-holder and

ruling-head are omitted

PLAN VIEW, SHOWING THE PLATE-CARRIAGE.

THE PLATE, PLATE-HOLDER AND RULING-HEAD ARE OMITTED,

Fig. 4

Side elevation opposite to Fig. i, showing the engine in the return

stroke position

Fia4. .

SIDE ELEVATION OPPOSITE TO Fia 1, SHOWING THE ENGINE IN THE RETURN STROKE POSITION.

CORRECTOR-FRAME IS SHOWN AS AN END VIEW,

INDEX

iN’um'bers refer to pages.

Al>erTatioiL Problems, 674.

Abney, Sir William de W., 491, 499,
574.

Absorption, Electric, 139, 297, 819,
321.

Absorption, Electric, of Crystals,
204.

Academy of Arts and Sciences,
American, 7, 343, 611.

Academy of Sciences, National, 1,
16, 610.

Academy, Prench, 411.

Aepinns, 626, 639.

Air-tbermometer, 358, 366.
Alternating Currents, 276, 280, 294,
314, 661.

Aniagat, E. H., 410.

Amaury (see Jamin), 344, 388.
Ames, J. S., 526, 661, 691.

AmpSre, 627, 639.

Anderson’s Method of Measuring
Resistance, 308.

Angstrom, A. J., 612, 613, 646, 553,
665 .

Angstrom’s Scale, 517, 563.

Arago, 642.

Archimedes, 619, 620, 621.
Atmospheric Eleotrioity, 183, 212.
Aurora, Spectrum of the, 2, 31.
Aurora, Theory of the, 179.

Ayrton, W. E., 179, 182, 183, 213, 278.

Basic Lines of Lockyer, 524.
Battery, Water, 241.

Baudin’s Thermometers, 364, 386,
466.

Becquerel, A. C., 184, 214.

Beek, A. Tan, 411.

Bell, Graham, 674.

Bell, Louis, 242, 613 et seq., 546, 646,
553 et seq.

Benzenberg, J. P., 411.

B€rard, J. E., 409, 410.

Berlin, University of, 4, 128.

Berlin Academy, 4.

Biot, J. B., 39, 90, 114, 116, 626, 627,
639.

Bosscha, J., 408, 465.

Boyle, Robert, 7.

Brashear, J. A., 9.

Bravais, A., 411.

Briggs, L. J., 671, 573.

B. A. Unit, 82, 84, 145, 146, 166, 217,
239.

Bruce, Miss, 621.

Calorimetry, 387.

Canton, John, 625.

Capacity, Electric, 297 ct seq-, 314
et seq.

Carmichael, N. R., 571, 573.
Cathetometer, 361.

Cavendish, Henry, 626, 039.

Cazin, A. A,, 36, 48, 410.

Chapman (see Rutherfurd), 8.
Chemical Reaction, Action of Mag-
net on, 242.

Clarke, P. W., 670.

Clausius, R. J. E., 204, 205, 210.
Client (see D6sormes), 410.
Colordeau, 249.

Concave Gratings, 488, 492, 606.
Condenser, Standard, 267.
Convection, Elecixic, 128, 138, 179,
261.

Copernicus, 614.

700

Index

Coulomb, 0. A., 95, 96, 103, 119, ISO,
133, 626, 639, 645.

CrSmieu, Y-, 5.

Crystals, Electric Absorption of,
204.

Crystals, Magnetic Properties of,
187.

J>.

Daniell, J. P., 641.

DaTy, Sir Humphiy, 638, 639, 644,
650.

De Morgan, 619.

Delarocbe, P., 409, 410.

Deluc, J. A., 387.

D4sonnes, C. B., 410.

Diamagnetism, 76, 184.

Distribution, Magnetic, 80, 85, 89.
Dividing Engines, 487, 508, 693.
Doppler’s Principle, 674.

Dub, C. J., 36.

Du Pay, 639.

Dulong, P. D., 438.

Duncan, Louis, 283.

Dupr^, Athanase, 410.

Earths, The Bare, 565.

Echelon Spectroscope, 590.
Edelmann, M. T., 266.

Edison’s Electric Liglit, 200.
Edlund, E., 408, 416, 632.

Electric Absorption, 139, 297, 319,
321.

Electric Absorption of Crystals,
204.

Electric Convection, 138, 138, 179,
251.

Electric Currents, Theory of, 663.
Electric Lights Edison’s, 200,
Electric Units, 10.

Electric Units, Ratio of, 266.
Electrical Congresses, 10, 212, 217.
Electricity, Theories of, 285, 636.
Electricity, Atmospheric, 183, 212.
Electrodynamometer, 268, 284, 294,
314.

Electrometer, Abso-lute, 266.
Elements in the Sun, 522.

Ellis, Wm., 367.

Energy, Conservation of, 2, 6, 24.
Energy of Alternating Currents,
283.

Ether, Properties of the, 290 et
seq., 338, 680, 686, 632, 667, 673.
Ethereal Motion, Resistance to,
338.

Expansion of Air under Constant
Volume, 410.

Pairbaim, Sir Wm., 416.

Faraday, M., 24, 26, 40, 43, 66, 89,
165, 184, 224, 242, 261, 286, 288,
289, 596, 604, 616, 626, 629, 630,
638 et seq., 660, 666.

Faraday’s Lines of Force, 37, 127,
286.

Farrand, 12.

Pastry’s Thermometers, 365, 386,
416.

Faure, 660.

Pavre, P. A., 408, 410, 421.

Fiske, Lieut., 238.

Fitzgerald, G. F., 229, 231.
Flaugergues, H., 387.

Fleming, J. A., 278.

Fletcher, L. B., 266.
Fortin-barometer, 362.

Foster, Henry, 411.

Foucault, J. B, D., 674,
Foucault-currents, 219, 234.
Frankfort - LaufEen lExperiments,
284.

Franklin, Benjamin, 625, 639, 663,
665, 669.

Fraunhofer, J., 7.

Fresnel, A., 580.

Friction Brake, 423.

G-.

Galileo, 614.

Galvani, 626, 630.

Galvanometers, 40, 169, 166, 268.
Gaugain, J. M., 42.

Gauss, 97, 148, 181, 626.

Gay Lussac, 410.

Qeissler Thermometers, 465, 478,
481.

Ghosts in Spectra, 490, 492, 510, 619,
536.

Gibbs, O. Walcott, 364, 670.

Gilbert, N. E., 338,

Gilbert, William, 624, 639.

Gilman, D. C., 14, 15.

Glazebrook, E. T., 240, 506.

Index

701

Goldingham, John, 411.

Gramme Armatiare, 222, 224, 227,
228.

Gratings, 7, 487, 492, 687, 625.
Gratings, Concave, 488, 492, 605.
Gratings, Nobert, 8, 655.

Gratings, Manufacture of, 487, 508,
693.

Gratings, Use of, 519.

Gratings, Wandschaft’s, 649.
Gratingr-spectroscope, 489, 499, 512,
551, 588.

Gravitation, Cause of, 292.
Gravitation, Law of, 670.

Gray, Stephen, 624, 630, 653.

Green, George, 39, 90, 108, 114, 115,
116, 627, 630.

Green, James, 362.

Grooves in Gratings, Theory of,
529 et seq.

Guerricke, Otto v., 639.

Hall, E. H., 197, 266.

Hall EfEect, The, 197.

Harmonics in Alternating Cur-
rents, 276, 280, 300, 301.

Harris Unit Jar, 208, 200.

Harrison, C. N., 685.

Harvard University, 5.

Hastings, C. S., 7, 503.

Heat, Mechanical Eqiiivalcnt of, 5,
343 et seq., 469.

Heaviside, Oliver, 674.

Helmholtz, H. von, 4, 20, 83, 128,
131, 138, 160, 167, 170, 251, 314,
586, 630, 643.

Henry, Joseph, 63, 578, 657, 669.
Hertz, H., 289, 680, 058, 659, 673, 674.
Herwig, H. A. B., 416.

Hidden, 570.

Himstedt, E., 6.

Him, G. A., 344, 388, 408, 410, 416,
418, 423, 424.

Holman, S. W., 364, 384. .
Hutchinson, C. T., 4, 261.
Hysteresis, 276 et seq., 281.

Icilius, Quintus, 36, 408, 418.
Inductance, Measurement of, 294
et seq., 314, 325.

Ionization of Gases, 579.

Jacobi, M. H. v., 36.

Jacobi Unit, 147.

Jacques, W. W., 80, 81, 145, 174, 184,
193.

Jamin, J. C., 71, 80, 81, 89, 90, 96, 97,
122 et seq., 344, 388, 410.

Jenldn, Fleming, 150, 109.

Jewell. L. E‘., 524, 645, 650.

Johns Hopkins University, 4.

Jolly, P. G., 410.

Joule, 6, 7, 24, 27, 36, 52, 53, 146, ,344,
381, 408, 414, 416, 417, 419, 421,
460.

Joule’s Thermometers, 417, 469.

ISL

Kelvin, Lord (sec Thomson, Sir
William).

Kempf, P., 646, 653, 556.

Kew Thermometers, 363, 366, 381,
466.

Kimball, A. L., 239.

KirchholT, G. R., 145, 166, 239, 410,
628.

Koenig, Rudolph, 20, 217.

Kohlrausch, F. W., 4, 82, 83, 84, 146
et seq., 410, 421, 628.

Koyl, C. A., 549, 565.

Kriiss, Dr., 506, 570.

Kurlbaum, F., 546, 553, 554, 655.

Laboratories, Physical, 014.
Laboulaye, 0. P. L. do, 410.
Langley, S, P., 491.

Laplace, 025, 639, 571.

Lecher, E., 4, 252.

Lenard, P., 575, 585.

Lenz, H. F. E., 36, 408, 418.
Lightning, 230,

Lightning-rods, 237, 663.
Lippmann, G., 5.

Ijockyer, Sir J. Norman, 487, 524.
Lodge, Sir O. J., 602, 064, 674.
Lorenz, L. V., 146, 165, 156, 217, 239,
419.

Magnetic Circuit, 3, 38, 89, 225, 276.
Magnetic Distribution, 80, 85, 80.

Index

Magnetic Induction, Measurement
of, 98.

Magnetic Permeability, 35, 66,
Magnetic Proof Plane, 86.
Magnetism of Barth, 179, 313.
Magnetism, Cause of, 673.

Magnets, Lifting Power of, 63.
Magnets and Chemical Eeactions,
343.

Magnetization, Maximum, 35, 56.
Magnetization, Temporary, 49.
Magnus, H. G., 410.

Marcou, P. B., 316.

Marianini, S. G., 71.

Martins, 0. F., 411.

Mascart, E., 340.

Masson, A. P., 410.

Matthiessen, A., 147.

*MaxweU, J. C., 3, 63, 67, 71, 83, 89,
114, 138, 139, 149, 170, 198, 199,
334, 351, 389, 580, 660, 673.
Maxwell’s Electromagnetic The-
ory, 7, 198, 199, 389, 630, 631.
Mayer, Alfred M., 669.

Mayer, J. R., 34.

McFarlane, D., 437, 438.

McJunckin, P. C., 338.

Mechanical Equiyalent of Heat,
343, 469.

Mendenhall, T. C., 1.

Michelson, A. A,, 684, 590, 674.
Michie, Professor, 15.

Moll, G., 411.

Motors, Electric, 380, 381.

Muller, G., 546, 653, 565.

Muller, J. H. J., 36, 36, 48.
Munchausen, v., 344, 389.

Murphy, Robert 636.

Myrback, v., 411.

Tsr.

National Academy of Sciences, 1,
15, 610.

Nesbit, 63.

Neumann, F. E., 146, 387,
Neumann’s Coefficient, 35, 67, 73,
116.

Newton, Sir Isaac, 66, 386, 393, 615,
633, 638, 671.

Nichol, J. P., 436, 437, 438.

Nichols, E. L., 304, 349, 360.

Niven’s Method of Measuring In-
ductance, 309.

Nobert Gratings, 8, 656.

Oersted, 636, 639, 640.

Ohm, Determination of the, 317,
339, 419, 638.

Ohm’s Law for Currents, 139, 141,
238, 640.

Ohm’s Law for Magnetic Induc-
tion, 3, 38, 89, 90.

Paine’s Electromagnetic Engine,
34.

Parry, E., Capt., 411.

Peirce, C. S., 493, 494, 513 et seq.,
646 et seq.

Penniman, T. D., 397, 398, 314.
Permeability, Magnetic, 35, 56, 73.
Perry, John, 179, 183, 183, 313.

Petit, P., 438.

Pfaundler, L., 344, 351, 388, 467.
Phillips Academy, Andover, 11.
Pickering, E. C., 364.

Pickering, W., 343.

Plants, G., 650.

Platter (see Pfaundler), 344, 351,
388, 467.

Pliicker, J., 184.

PoggendorfC, J. C., 348-
PoisBon, 636, 630, 639.

Porous Plug Experiment, 346.
Porter, A. W., 580. ,

Power, Transmission of, 380.
Proof Plane, Magnetic, 85.

Puluj, J., 408, 424,

Pupin, M. I., 684, 685, 586.

Radiation of Heat, 435.

Rankine, W. J. M., 381.

Rayleigh, Lord, 340, 394, 535, 538,
534, 588, 638.

Rays, Rontgen, 671, 673, 676.
Recknagel, G. F., 356, 358, 389.
Regnault, V., 344, 353 et seq., 365,
368, 376, 388 et seq., 409 et seq.,
466, 607.

Remsen, Ira, 343 et seq.

* Keferonoes to Maxwell are so numerous that only the more Important ones are noted here-

Index

703

Bensselaer Folyteclmic Institute,

2 , 12 .

Resistance, Electrical; EjQEect of
Ma^etlc field on, 338.
Resistance, Electrical; Measure-
ment of, 313.

Resolving Pov^er, 502, 528, 588.
Resonances, 2, 28.

Richard (see Jamin), 410.

Riecke, E., 36.

Ritter, J. W., 639, 650.

Rontgen, W. C., 4, 252, 410, 414.
Rontgen-rays, 571, 673, 576.

Rogers, W. A., 441, 507.

Rosa, E. B., 266.

Royal Society of London, 3.
Ruling Engines, 8, 487, 508, 691.
Rumford, Count, 6, 408, 416, 669.
Rumford-fund, 7, 343, 621, 548.
Rutherfurd, L. W., 8, 487, 494, 513.

Savart, E., 411, 627.

Schiller, N. N., 262.

Schneider, Theodore, 9, 487, 692.
Scott, 0. E., 237.

Screws, Perfect, 8, 487, 506.

Sears, David, 80, 98.

Seebeck, L. E. W. A., 134, 640.
Shroder v. d. Kolk, 411, 414.
Siemens Armature, 210, 221, 222,
228.

Siemens Unit, 4, 147, 162, 156, 156.
Silbermnnn, J. T., 408, 410, 421.

« Skin-Effect ” of Alternating Cur-
rents, 283, 661.

Solar Spectrum, 9, 512, 521.

Sound, Velocity of, 411.

Specific Heats of Air, Ratio of, 410.
Specific Heats of Gases, 409, 410.
Specific Heat of Water, 387.
Spectroscope, Co*cave Grating, 489,
499, 512, 551, 589.

Spectroscoi)e, Plane Grating, 688.
Spectrum of the Aurora, 2, 31.
Spectrum, Solar, 512, 621.

Stompfer, S., 411.

Stefan, J., 69.

Steinheil, 166, 168.

Steinmetz, C. P., 278.

Stokes, Sir G. G., 674.

Stoletow, A. G., 36, 48, 50, 71, 73, 91,
105, 154.

Sturgeon, William, 63.

Tate, T., 416.

Tatnall, R. R., 686.

Telegraph, Multiplex Printing, 10.
Temperature, Absolute Scale of,
381.

Temperature, Effect of, on Mag-
netization, 58, 65, 74.

Tesla, Nicola, 678.

Thal6n, T. R., 613, 646, 556.
Thermometers, Air, 358, 366.
Thermometers, Mercurial, 346, 363.
Thermometers, Mercurial and air,
352.

Thermometers, Comparisons of,
477.

Thermometers, Standard, 363.
Thermometry, 346, 439.

Thiessen, M. E., 481.

Thompson, S. P., 233, 234, 235.
Thomson, Elihu, 232, 235, 573, 574,
584, 585.

Thomson, J. J., 679, 674.
^^Thomson, Sir William, 37, 77, 78.
79, 148, 213, 346, 381, 414, 421,
626, 649, 657.

Thunderstorms, Theory of, 183, 213.
Transformers, Theory of, 276, 280.
Tresca, H. E., 410, 613.
Trowbridge, John, 216, 364.
Tyndall, John, 26, 27, 97, 574, 641.

Venetian Institute; Prize Essay, 7.
Verdet, M. E., 58, 79.

Violle, J. L. G., 408, 418.

Vogel, H. C., 649, 666, 667.

Volta, 620, 639,. 645.

Vortex in Outlet of Water, 23.

Waldo, L., 481.

Waltenhofen, A. H., 421.
Wandschaft’s Gratings, 549.

Water, Specific Heat of, 387.
Water Battery, 241.

* The referenoes to lord Kelvin ore so numerous that only the Important ones are noted
here.

704 :

IlfDBX

Wave-lengtlis, Standard, 613, 517,
621, 546, 548.

Webb, R C., 38,

Weber, 36, 48, 49, 126, 137, 147, 148,
152, 153, 166, 160, 170. 184, 240,
408, 418, 419, 626, 628.

Weber, H. P., 166, 408, 418, 419, 420.
Weisbach, J., 410.

Welsk’s Thermometers, 365,
Welter, J. J., 410.

West Point Military Academy, 14.
Wheatstone, C., 649.

Wiedemann, B., 409, 415.

Wiedemann, G., 240.
Wilke, J. K., 639.
Wollaston, W. H., 604.
WuUner, A., 368, 410.

Yale University, 11.
Yoimg-, C. A., 487, 493.
Young, Thomas, 7.

Zieman EfEect, 672, 673-

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